diff --git a/docs/recommendations/06a0ba437d41a7c82c08a9636a4438c1b5031378.md b/docs/recommendations/06a0ba437d41a7c82c08a9636a4438c1b5031378.md
index c2bda480..678930fd 100644
--- a/docs/recommendations/06a0ba437d41a7c82c08a9636a4438c1b5031378.md
+++ b/docs/recommendations/06a0ba437d41a7c82c08a9636a4438c1b5031378.md
@@ -11,7 +11,7 @@ hide:
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-12-30 06:05:43 UTC</i>
+  <i class="footer">This page was last updated on 2025-01-06 06:05:58 UTC</i>
   </p>
   
   <div class="note info" onclick="startIntro()">
@@ -110,7 +110,7 @@ hide:
           </td>
           <td>2022-06-01</td>
           <td>Nonlinear Dynamics</td>
-          <td>31</td>
+          <td>32</td>
           <td>93</td>
         </tr>
     
diff --git a/docs/recommendations/0acd117521ef5aafb09fed02ab415523b330b058.md b/docs/recommendations/0acd117521ef5aafb09fed02ab415523b330b058.md
index 6efb1037..18782c85 100644
--- a/docs/recommendations/0acd117521ef5aafb09fed02ab415523b330b058.md
+++ b/docs/recommendations/0acd117521ef5aafb09fed02ab415523b330b058.md
@@ -11,7 +11,7 @@ hide:
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-12-30 06:05:46 UTC</i>
+  <i class="footer">This page was last updated on 2025-01-06 06:06:10 UTC</i>
   </p>
   
   <div class="note info" onclick="startIntro()">
@@ -74,7 +74,7 @@ hide:
           </td>
           <td>2015-09-11</td>
           <td>Proceedings of the National Academy of Sciences</td>
-          <td>3476</td>
+          <td>3490</td>
           <td>68</td>
         </tr>
     
@@ -98,7 +98,7 @@ hide:
           </td>
           <td>2020-05-05</td>
           <td>Nature Communications</td>
-          <td>301</td>
+          <td>305</td>
           <td>13</td>
         </tr>
     
diff --git a/docs/recommendations/0d01d21137a5af9f04e4b16a55a0f732cb8a540b.md b/docs/recommendations/0d01d21137a5af9f04e4b16a55a0f732cb8a540b.md
index 5de4bd9d..6ec7abdb 100644
--- a/docs/recommendations/0d01d21137a5af9f04e4b16a55a0f732cb8a540b.md
+++ b/docs/recommendations/0d01d21137a5af9f04e4b16a55a0f732cb8a540b.md
@@ -11,7 +11,7 @@ hide:
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-12-30 06:05:19 UTC</i>
+  <i class="footer">This page was last updated on 2025-01-06 06:05:39 UTC</i>
   </p>
   
   <div class="note info" onclick="startIntro()">
diff --git a/docs/recommendations/123acfbccca0460171b6b06a4012dbb991cde55b.md b/docs/recommendations/123acfbccca0460171b6b06a4012dbb991cde55b.md
index a026f01a..fb2f97b7 100644
--- a/docs/recommendations/123acfbccca0460171b6b06a4012dbb991cde55b.md
+++ b/docs/recommendations/123acfbccca0460171b6b06a4012dbb991cde55b.md
@@ -11,7 +11,7 @@ hide:
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-12-30 06:05:20 UTC</i>
+  <i class="footer">This page was last updated on 2025-01-06 06:05:40 UTC</i>
   </p>
   
   <div class="note info" onclick="startIntro()">
@@ -50,7 +50,7 @@ hide:
           </td>
           <td>2024-03-12</td>
           <td>ArXiv</td>
-          <td>82</td>
+          <td>85</td>
           <td>18</td>
         </tr>
     
@@ -62,7 +62,7 @@ hide:
           </td>
           <td>2024-02-04</td>
           <td>ArXiv</td>
-          <td>6</td>
+          <td>7</td>
           <td>67</td>
         </tr>
     
@@ -109,7 +109,7 @@ hide:
             Yong Liu, Haoran Zhang, Chenyu Li, Xiangdong Huang, Jianmin Wang, Mingsheng Long
           </td>
           <td>2024-02-04</td>
-          <td>ArXiv, DBLP</td>
+          <td>DBLP, ArXiv</td>
           <td>26</td>
           <td>67</td>
         </tr>
@@ -122,7 +122,7 @@ hide:
           </td>
           <td>2023-10-05</td>
           <td>ArXiv</td>
-          <td>65</td>
+          <td>66</td>
           <td>5</td>
         </tr>
     
diff --git a/docs/recommendations/16f01c1b3ddd0b2abd5ddfe4fdb3f74767607277.md b/docs/recommendations/16f01c1b3ddd0b2abd5ddfe4fdb3f74767607277.md
index eaef36a9..fbbfab66 100644
--- a/docs/recommendations/16f01c1b3ddd0b2abd5ddfe4fdb3f74767607277.md
+++ b/docs/recommendations/16f01c1b3ddd0b2abd5ddfe4fdb3f74767607277.md
@@ -11,7 +11,7 @@ hide:
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-12-30 06:05:24 UTC</i>
+  <i class="footer">This page was last updated on 2025-01-06 06:05:42 UTC</i>
   </p>
   
   <div class="note info" onclick="startIntro()">
@@ -86,7 +86,7 @@ hide:
           </td>
           <td>2022-09-20</td>
           <td>IEEE Transactions on Knowledge and Data Engineering</td>
-          <td>90</td>
+          <td>91</td>
           <td>18</td>
         </tr>
     
@@ -110,7 +110,7 @@ hide:
           </td>
           <td>2024-05-03</td>
           <td>ArXiv</td>
-          <td>13</td>
+          <td>14</td>
           <td>47</td>
         </tr>
     
diff --git a/docs/recommendations/1df04f33a8ef313cc2067147dbb79c3ca7c5c99f.md b/docs/recommendations/1df04f33a8ef313cc2067147dbb79c3ca7c5c99f.md
index 9254aee3..77fbc034 100644
--- a/docs/recommendations/1df04f33a8ef313cc2067147dbb79c3ca7c5c99f.md
+++ b/docs/recommendations/1df04f33a8ef313cc2067147dbb79c3ca7c5c99f.md
@@ -11,7 +11,7 @@ hide:
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-12-30 06:05:21 UTC</i>
+  <i class="footer">This page was last updated on 2025-01-06 06:05:41 UTC</i>
   </p>
   
   <div class="note info" onclick="startIntro()">
@@ -62,7 +62,7 @@ hide:
           </td>
           <td>2024-02-13</td>
           <td>ArXiv, DBLP</td>
-          <td>43</td>
+          <td>42</td>
           <td>9</td>
         </tr>
     
@@ -86,7 +86,7 @@ hide:
           </td>
           <td>2024-06-09</td>
           <td>ArXiv</td>
-          <td>4</td>
+          <td>5</td>
           <td>4</td>
         </tr>
     
diff --git a/docs/recommendations/279cd637b7e38bba1dd8915b5ce68cbcacecbe68.md b/docs/recommendations/279cd637b7e38bba1dd8915b5ce68cbcacecbe68.md
index 1f8b94dd..44b79177 100644
--- a/docs/recommendations/279cd637b7e38bba1dd8915b5ce68cbcacecbe68.md
+++ b/docs/recommendations/279cd637b7e38bba1dd8915b5ce68cbcacecbe68.md
@@ -11,7 +11,7 @@ hide:
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-12-30 06:05:28 UTC</i>
+  <i class="footer">This page was last updated on 2025-01-06 06:05:45 UTC</i>
   </p>
   
   <div class="note info" onclick="startIntro()">
@@ -49,7 +49,7 @@ hide:
             Andreas Doerr, Christian Daniel, Martin Schiegg, D. Nguyen-Tuong, S. Schaal, Marc Toussaint, Sebastian Trimpe
           </td>
           <td>2018-01-31</td>
-          <td>ArXiv, DBLP, MAG</td>
+          <td>DBLP, ArXiv, MAG</td>
           <td>115</td>
           <td>93</td>
         </tr>
@@ -102,18 +102,6 @@ hide:
           <td>50</td>
         </tr>
     
-        <tr id="Forecasting the behaviour of complex dynamical systems such as interconnected sensor networks characterized by high-dimensional multivariate time series(MTS) is of paramount importance for making informed decisions and planning for the future in a broad spectrum of applications. Graph forecasting networks(GFNs) are well-suited for forecasting MTS data that exhibit spatio-temporal dependencies. However, most prior works of GFN-based methods on MTS forecasting rely on domain-expertise to model the nonlinear dynamics of the system, but neglect the potential to leverage the inherent relational-structural dependencies among time series variables underlying MTS data. On the other hand, contemporary works attempt to infer the relational structure of the complex dependencies between the variables and simultaneously learn the nonlinear dynamics of the interconnected system but neglect the possibility of incorporating domain-specific prior knowledge to improve forecast accuracy. To this end, we propose a hybrid architecture that combines explicit prior knowledge with implicit knowledge of the relational structure within the MTS data. It jointly learns intra-series temporal dependencies and inter-series spatial dependencies by encoding time-conditioned structural spatio-temporal inductive biases to provide more accurate and reliable forecasts. It also models the time-varying uncertainty of the multi-horizon forecasts to support decision-making by providing estimates of prediction uncertainty. The proposed architecture has shown promising results on multiple benchmark datasets and outperforms state-of-the-art forecasting methods by a significant margin. We report and discuss the ablation studies to validate our forecasting architecture.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/05cd3afc8208f1c0dd61b09a90f35dd42497e175" target='_blank'>Multi-Knowledge Fusion Network for Time Series Representation Learning</a></td>
-          <td>
-            Sakhinana Sagar Srinivas, Shivam Gupta, Krishna Sai Sudhir Aripirala, Venkataramana Runkana
-          </td>
-          <td>2024-08-22</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>3</td>
-        </tr>
-    
         <tr id="Real-world dynamical systems often consist of multiple stochastic subsystems that interact with each other. Modeling and forecasting the behavior of such dynamics are generally not easy, due to the inherent hardness in understanding the complicated interactions and evolutions of their constituents. This paper introduces the relational state-space model (R-SSM), a sequential hierarchical latent variable model that makes use of graph neural networks (GNNs) to simulate the joint state transitions of multiple correlated objects. By letting GNNs cooperate with SSM, R-SSM provides a flexible way to incorporate relational information into the modeling of multi-object dynamics. We further suggest augmenting the model with normalizing flows instantiated for vertex-indexed random variables and propose two auxiliary contrastive objectives to facilitate the learning. The utility of R-SSM is empirically evaluated on synthetic and real time series datasets.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
           <td><a href="https://www.semanticscholar.org/paper/7a1e5377b08489c2969f73c56efc557e34f578e1" target='_blank'>Relational State-Space Model for Stochastic Multi-Object Systems</a></td>
@@ -126,16 +114,32 @@ hide:
           <td>61</td>
         </tr>
     
-        <tr id="Over the past few years, research on deep graph learning has shifted from static graphs to temporal graphs in response to real-world complex systems that exhibit dynamic behaviors. In practice, temporal graphs are formalized as an ordered sequence of static graph snapshots observed at discrete time points. Sequence models such as RNNs or Transformers have long been the predominant backbone networks for modeling such temporal graphs. Yet, despite the promising results, RNNs struggle with long-range dependencies, while transformers are burdened by quadratic computational complexity. Recently, state space models (SSMs), which are framed as discretized representations of an underlying continuous-time linear dynamical system, have garnered substantial attention and achieved breakthrough advancements in independent sequence modeling. In this work, we undertake a principled investigation that extends SSM theory to temporal graphs by integrating structural information into the online approximation objective via the adoption of a Laplacian regularization term. The emergent continuous-time system introduces novel algorithmic challenges, thereby necessitating our development of GraphSSM, a graph state space model for modeling the dynamics of temporal graphs. Extensive experimental results demonstrate the effectiveness of our GraphSSM framework across various temporal graph benchmarks.">
+        <tr id="Time series modeling is a well-established problem, which often requires that methods (1) expressively represent complicated dependencies, (2) forecast long horizons, and (3) efficiently train over long sequences. State-space models (SSMs) are classical models for time series, and prior works combine SSMs with deep learning layers for efficient sequence modeling. However, we find fundamental limitations with these prior approaches, proving their SSM representations cannot express autoregressive time series processes. We thus introduce SpaceTime, a new state-space time series architecture that improves all three criteria. For expressivity, we propose a new SSM parameterization based on the companion matrix -- a canonical representation for discrete-time processes -- which enables SpaceTime's SSM layers to learn desirable autoregressive processes. For long horizon forecasting, we introduce a"closed-loop"variation of the companion SSM, which enables SpaceTime to predict many future time-steps by generating its own layer-wise inputs. For efficient training and inference, we introduce an algorithm that reduces the memory and compute of a forward pass with the companion matrix. With sequence length $\ell$ and state-space size $d$, we go from $\tilde{O}(d \ell)$ na\"ively to $\tilde{O}(d + \ell)$. In experiments, our contributions lead to state-of-the-art results on extensive and diverse benchmarks, with best or second-best AUROC on 6 / 7 ECG and speech time series classification, and best MSE on 14 / 16 Informer forecasting tasks. Furthermore, we find SpaceTime (1) fits AR($p$) processes that prior deep SSMs fail on, (2) forecasts notably more accurately on longer horizons than prior state-of-the-art, and (3) speeds up training on real-world ETTh1 data by 73% and 80% relative wall-clock time over Transformers and LSTMs.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/919e5db29c7b7be4468b975eb4c0fa4a543165fc" target='_blank'>State Space Models on Temporal Graphs: A First-Principles Study</a></td>
+          <td><a href="https://www.semanticscholar.org/paper/a7d68b1702af08ce4dbbf2cd0b083e744ae5c6be" target='_blank'>Effectively Modeling Time Series with Simple Discrete State Spaces</a></td>
           <td>
-            Jintang Li, Ruofan Wu, Xinzhou Jin, Boqun Ma, Liang Chen, Zibin Zheng
+            Michael Zhang, Khaled Kamal Saab, Michael Poli, Tri Dao, Karan Goel, Christopher Ré
           </td>
-          <td>2024-06-03</td>
+          <td>2023-03-16</td>
           <td>ArXiv</td>
-          <td>2</td>
-          <td>12</td>
+          <td>37</td>
+          <td>46</td>
+        </tr>
+    
+        <tr id="
+ 
+ Gaussian state space models have been used for decades as generative models of sequential data. They admit an intuitive probabilistic interpretation, have a simple functional form, and enjoy widespread adoption. We introduce a unified algorithm to efficiently learn a broad class of linear and non-linear state space models, including variants where the emission and transition distributions are modeled by deep neural networks. Our learning algorithm simultaneously learns a compiled inference network and the generative model, leveraging a structured variational approximation parameterized by recurrent neural networks to mimic the posterior distribution. We apply the learning algorithm to both synthetic and real-world datasets, demonstrating its scalability and versatility. We find that using the structured approximation to the posterior results in models with significantly higher held-out likelihood.
+ 
+">
+          <td id="tag"><i class="material-icons">visibility_off</i></td>
+          <td><a href="https://www.semanticscholar.org/paper/2af17f153e3fd71e15db9216b972aef222f46617" target='_blank'>Structured Inference Networks for Nonlinear State Space Models</a></td>
+          <td>
+            R. G. Krishnan, Uri Shalit, D. Sontag
+          </td>
+          <td>2016-09-30</td>
+          <td>DBLP, ArXiv, MAG</td>
+          <td>440</td>
+          <td>48</td>
         </tr>
     
   </tbody>
diff --git a/docs/recommendations/2b2aa13d4959073f61ad70555bc8c7da7d116196.md b/docs/recommendations/2b2aa13d4959073f61ad70555bc8c7da7d116196.md
index 59c9e3cd..051b1ef6 100644
--- a/docs/recommendations/2b2aa13d4959073f61ad70555bc8c7da7d116196.md
+++ b/docs/recommendations/2b2aa13d4959073f61ad70555bc8c7da7d116196.md
@@ -11,7 +11,7 @@ hide:
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-12-30 06:05:44 UTC</i>
+  <i class="footer">This page was last updated on 2025-01-06 06:05:59 UTC</i>
   </p>
   
   <div class="note info" onclick="startIntro()">
@@ -122,7 +122,7 @@ hide:
           </td>
           <td>2020-07-02</td>
           <td>ArXiv</td>
-          <td>140</td>
+          <td>142</td>
           <td>23</td>
         </tr>
     
@@ -134,7 +134,7 @@ hide:
           </td>
           <td>2020-03-17</td>
           <td>Autom.</td>
-          <td>18</td>
+          <td>19</td>
           <td>5</td>
         </tr>
     
@@ -159,7 +159,7 @@ hide:
           <td>2022-06-20</td>
           <td>Philosophical transactions. Series A, Mathematical, physical, and engineering sciences</td>
           <td>57</td>
-          <td>33</td>
+          <td>34</td>
         </tr>
     
   </tbody>
diff --git a/docs/recommendations/35e2571c17246577e0bc1b9de57a314c3b60e220.md b/docs/recommendations/35e2571c17246577e0bc1b9de57a314c3b60e220.md
index 3afff1e3..95be6ab2 100644
--- a/docs/recommendations/35e2571c17246577e0bc1b9de57a314c3b60e220.md
+++ b/docs/recommendations/35e2571c17246577e0bc1b9de57a314c3b60e220.md
@@ -11,7 +11,7 @@ hide:
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-12-30 06:05:46 UTC</i>
+  <i class="footer">This page was last updated on 2025-01-06 06:06:00 UTC</i>
   </p>
   
   <div class="note info" onclick="startIntro()">
@@ -109,7 +109,7 @@ hide:
             Philipp Holl, V. Koltun, Nils Thuerey
           </td>
           <td>2021-09-30</td>
-          <td>ArXiv, DBLP</td>
+          <td>DBLP, ArXiv</td>
           <td>6</td>
           <td>106</td>
         </tr>
@@ -150,16 +150,16 @@ hide:
           <td>17</td>
         </tr>
     
-        <tr id="None">
+        <tr id="Big data is transforming scientific progress by enabling the discovery of novel models, enhancing existing frameworks, and facilitating precise uncertainty quantification, while advancements in scientific machine learning complement this by providing powerful tools to solve inverse problems to identify the complex systems where traditional methods falter due to sparse or noisy data. We introduce two innovative neural operator frameworks tailored for discovering hidden physics and identifying unknown system parameters from sparse measurements. The first framework integrates a popular neural operator, DeepONet, and a physics-informed neural network to capture the relationship between sparse data and the underlying physics, enabling the accurate discovery of a family of governing equations. The second framework focuses on system parameter identification, leveraging a DeepONet pre-trained on sparse sensor measurements to initialize a physics-constrained inverse model. Both frameworks excel in handling limited data and preserving physical consistency. Benchmarking on the Burgers' equation and reaction-diffusion system demonstrates state-of-the-art performance, achieving average $L_2$ errors of $\mathcal{O}(10^{-2})$ for hidden physics discovery and absolute errors of $\mathcal{O}(10^{-3})$ for parameter identification. These results underscore the frameworks' robustness, efficiency, and potential for solving complex scientific problems with minimal observational data.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/55be4b71d7c8366b0f095e769f4586ce664c7415" target='_blank'>Discovering conservation laws using optimal transport and manifold learning</a></td>
+          <td><a href="https://www.semanticscholar.org/paper/fac52e25998ecb2657489d5358e6d0ca9064f2f7" target='_blank'>Learning Hidden Physics and System Parameters with Deep Operator Networks</a></td>
           <td>
-            Peter Y. Lu, Rumen Dangovski, M. Soljavci'c
+            Vijay Kag, Dibakar Roy Sarkar, Birupaksha Pal, Somdatta Goswami
           </td>
-          <td>2022-08-31</td>
-          <td>Nature Communications</td>
-          <td>12</td>
-          <td>13</td>
+          <td>2024-12-06</td>
+          <td>ArXiv</td>
+          <td>0</td>
+          <td>0</td>
         </tr>
     
   </tbody>
diff --git a/docs/recommendations/3c9961153493370500020c81527b3548c96f81e0.md b/docs/recommendations/3c9961153493370500020c81527b3548c96f81e0.md
index adaf30f1..b164a95a 100644
--- a/docs/recommendations/3c9961153493370500020c81527b3548c96f81e0.md
+++ b/docs/recommendations/3c9961153493370500020c81527b3548c96f81e0.md
@@ -11,7 +11,7 @@ hide:
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-12-30 06:05:39 UTC</i>
+  <i class="footer">This page was last updated on 2025-01-06 06:05:57 UTC</i>
   </p>
   
   <div class="note info" onclick="startIntro()">
@@ -50,7 +50,7 @@ hide:
           </td>
           <td>2015-09-11</td>
           <td>Proceedings of the National Academy of Sciences</td>
-          <td>3476</td>
+          <td>3490</td>
           <td>68</td>
         </tr>
     
@@ -62,7 +62,7 @@ hide:
           </td>
           <td>2020-05-05</td>
           <td>Nature Communications</td>
-          <td>301</td>
+          <td>305</td>
           <td>13</td>
         </tr>
     
diff --git a/docs/recommendations/3df50e9b73cc2937dfd651f4c3344bc99b7ed3f2.md b/docs/recommendations/3df50e9b73cc2937dfd651f4c3344bc99b7ed3f2.md
index cf3a4704..b2544832 100644
--- a/docs/recommendations/3df50e9b73cc2937dfd651f4c3344bc99b7ed3f2.md
+++ b/docs/recommendations/3df50e9b73cc2937dfd651f4c3344bc99b7ed3f2.md
@@ -11,7 +11,7 @@ hide:
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-12-30 06:05:40 UTC</i>
+  <i class="footer">This page was last updated on 2025-01-06 06:05:57 UTC</i>
   </p>
   
   <div class="note info" onclick="startIntro()">
@@ -74,7 +74,7 @@ hide:
           </td>
           <td>2022-01-13</td>
           <td>Proceedings of the Royal Society A</td>
-          <td>76</td>
+          <td>77</td>
           <td>68</td>
         </tr>
     
@@ -102,6 +102,18 @@ hide:
           <td>83</td>
         </tr>
     
+        <tr id="Many complex phenomena, from weather systems to heartbeat rhythm patterns, are effectively modeled as low-dimensional dynamical systems. Such systems may behave chaotically under certain conditions, and so the ability to detect chaos based on empirical measurement is an important step in characterizing and predicting these processes. Classifying a system as chaotic usually requires estimating its largest Lyapunov exponent, which quantifies the average rate of convergence or divergence of initially close trajectories in state space, and for which a positive value is generally accepted as an operational definition of chaos. Estimating the largest Lyapunov exponent from observations of a process is especially challenging in systems affected by dynamical noise, which is the case for many models of real-world processes, in particular models of biological systems. We describe a novel method for estimating the largest Lyapunov exponent from data, based on training Deep Learning models on synthetically generated trajectories, and demonstrate that this method yields accurate and noise-robust predictions given relatively short inputs and across a range of different dynamical systems. Our method is unique in that it can analyze tree-shaped data, a ubiquitous topology in biological settings, and specifically in dynamics over lineages of cells or organisms. We also characterize the types of input information extracted by our models for their predictions, allowing for a deeper understanding into the different ways by which chaos can be analyzed in different topologies.">
+          <td id="tag"><i class="material-icons">visibility_off</i></td>
+          <td><a href="https://www.semanticscholar.org/paper/9fb357e57624525f27224822502061cc8fb831e1" target='_blank'>Detecting chaos in lineage-trees: A deep learning approach</a></td>
+          <td>
+            H. Rappeport, Irit Levin Reisman, Naftali Tishby, N. Balaban
+          </td>
+          <td>2021-06-08</td>
+          <td>ArXiv</td>
+          <td>3</td>
+          <td>56</td>
+        </tr>
+    
         <tr id="A generally applicable robust data-driven network modeling strategy offers rapid means to predict and control complex systems. We propose a universal method for data-driven modeling of complex nonlinear dynamics from time-resolved snapshot data without prior knowledge. Complex nonlinear dynamics govern many fields of science and engineering. Data-driven dynamic modeling often assumes a low-dimensional subspace or manifold for the state. We liberate ourselves from this assumption by proposing cluster-based network modeling (CNM) bridging machine learning, network science, and statistical physics. CNM describes short- and long-term behavior and is fully automatable, as it does not rely on application-specific knowledge. CNM is demonstrated for the Lorenz attractor, ECG heartbeat signals, Kolmogorov flow, and a high-dimensional actuated turbulent boundary layer. Even the notoriously difficult modeling benchmark of rare events in the Kolmogorov flow is solved. This automatable universal data-driven representation of complex nonlinear dynamics complements and expands network connectivity science and promises new fast-track avenues to understand, estimate, predict, and control complex systems in all scientific fields.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
           <td><a href="https://www.semanticscholar.org/paper/b0c3d159c14b0488299269c3fd62da3b9f608709" target='_blank'>Cluster-based network modeling—From snapshots to complex dynamical systems</a></td>
diff --git a/docs/recommendations/455bfc515eb279cc09023faa1f78c6efb61224ba.md b/docs/recommendations/455bfc515eb279cc09023faa1f78c6efb61224ba.md
index fb2e80a5..5e00f29e 100644
--- a/docs/recommendations/455bfc515eb279cc09023faa1f78c6efb61224ba.md
+++ b/docs/recommendations/455bfc515eb279cc09023faa1f78c6efb61224ba.md
@@ -11,7 +11,7 @@ hide:
 
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   <p>
-  <i class="footer">This page was last updated on 2024-12-30 06:05:17 UTC</i>
+  <i class="footer">This page was last updated on 2025-01-06 06:05:37 UTC</i>
   </p>
   
   <div class="note info" onclick="startIntro()">
@@ -145,7 +145,7 @@ hide:
             Steven Cheng-Xian Li, Benjamin M Marlin
           </td>
           <td>2020-07-12</td>
-          <td>ArXiv, DBLP, MAG</td>
+          <td>MAG, ArXiv, DBLP</td>
           <td>55</td>
           <td>34</td>
         </tr>
diff --git a/docs/recommendations/4971f9abd024e40fbbdff2e9492745b68a6bca01.md b/docs/recommendations/4971f9abd024e40fbbdff2e9492745b68a6bca01.md
index 37156f01..3852372b 100644
--- a/docs/recommendations/4971f9abd024e40fbbdff2e9492745b68a6bca01.md
+++ b/docs/recommendations/4971f9abd024e40fbbdff2e9492745b68a6bca01.md
@@ -11,7 +11,7 @@ hide:
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-12-30 06:05:44 UTC</i>
+  <i class="footer">This page was last updated on 2025-01-06 06:05:59 UTC</i>
   </p>
   
   <div class="note info" onclick="startIntro()">
@@ -51,7 +51,7 @@ hide:
           <td>2022-09-04</td>
           <td>Scientific Reports</td>
           <td>4</td>
-          <td>24</td>
+          <td>25</td>
         </tr>
     
         <tr id="Modern societies have an abundance of data yet good system models are rare. Unfortunately, many of the current system identification and machine learning techniques fail to generalize outside of the training set, producing models that violate basic physical laws. This work proposes a novel method for the Sparse Identification of Nonlinear Dynamics with Side Information (SINDy-SI). SINDy-SI is an iterative method that uses Sum-of-Squares (SOS) programming to learn optimally fitted models while guaranteeing that the learned model satisfies side information, such as symmetries and physical laws. Guided by the principle of Occam's razor, that the simplest or most regularized best fitted model is typically the superior choice, during each iteration SINDy-SI prunes the basis functions associated with small coefficients, yielding a sparse dynamical model upon termination. Through several numerical experiments we will show how the combination of side information constraints and sparse polynomial representation cultivates dynamical models that obey known physical laws while displaying impressive generalized performance beyond the training set.">
@@ -74,7 +74,7 @@ hide:
           </td>
           <td>2021-11-12</td>
           <td>J. Open Source Softw.</td>
-          <td>124</td>
+          <td>125</td>
           <td>68</td>
         </tr>
     
@@ -87,7 +87,7 @@ hide:
           <td>2020-01-31</td>
           <td>IEEE Robotics and Automation Letters</td>
           <td>24</td>
-          <td>24</td>
+          <td>25</td>
         </tr>
     
         <tr id="None">
@@ -110,7 +110,7 @@ hide:
           </td>
           <td>2022-11-10</td>
           <td>SSRN Electronic Journal</td>
-          <td>15</td>
+          <td>17</td>
           <td>33</td>
         </tr>
     
diff --git a/docs/recommendations/4a111f7a3b56d0468f13104999844885157ef17d.md b/docs/recommendations/4a111f7a3b56d0468f13104999844885157ef17d.md
index 31f43c9b..9f931b9d 100644
--- a/docs/recommendations/4a111f7a3b56d0468f13104999844885157ef17d.md
+++ b/docs/recommendations/4a111f7a3b56d0468f13104999844885157ef17d.md
@@ -11,7 +11,7 @@ hide:
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-12-30 06:05:23 UTC</i>
+  <i class="footer">This page was last updated on 2025-01-06 06:05:42 UTC</i>
   </p>
   
   <div class="note info" onclick="startIntro()">
@@ -86,7 +86,7 @@ hide:
           </td>
           <td>2024-03-12</td>
           <td>ArXiv</td>
-          <td>82</td>
+          <td>85</td>
           <td>18</td>
         </tr>
     
@@ -97,7 +97,7 @@ hide:
             Yong Liu, Haoran Zhang, Chenyu Li, Xiangdong Huang, Jianmin Wang, Mingsheng Long
           </td>
           <td>2024-02-04</td>
-          <td>ArXiv, DBLP</td>
+          <td>DBLP, ArXiv</td>
           <td>26</td>
           <td>67</td>
         </tr>
@@ -110,7 +110,7 @@ hide:
           </td>
           <td>2022-11-27</td>
           <td>ArXiv</td>
-          <td>777</td>
+          <td>784</td>
           <td>35</td>
         </tr>
     
diff --git a/docs/recommendations/5bd2c0acaf58c25f71617db2396188c74d29bf14.md b/docs/recommendations/5bd2c0acaf58c25f71617db2396188c74d29bf14.md
index 51662d55..5512a090 100644
--- a/docs/recommendations/5bd2c0acaf58c25f71617db2396188c74d29bf14.md
+++ b/docs/recommendations/5bd2c0acaf58c25f71617db2396188c74d29bf14.md
@@ -11,7 +11,7 @@ hide:
 
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   <p>
-  <i class="footer">This page was last updated on 2024-12-30 06:05:27 UTC</i>
+  <i class="footer">This page was last updated on 2025-01-06 06:05:44 UTC</i>
   </p>
   
   <div class="note info" onclick="startIntro()">
@@ -74,7 +74,7 @@ hide:
           </td>
           <td>2022-03-15</td>
           <td>ACM Transactions on Knowledge Discovery from Data</td>
-          <td>53</td>
+          <td>55</td>
           <td>40</td>
         </tr>
     
@@ -121,7 +121,7 @@ hide:
             Xiaoyong Jin, Youngsuk Park, Danielle C. Maddix, Bernie Wang, Xifeng Yan
           </td>
           <td>2021-02-13</td>
-          <td>ArXiv, DBLP</td>
+          <td>DBLP, ArXiv</td>
           <td>65</td>
           <td>66</td>
         </tr>
diff --git a/docs/recommendations/5d150cec2775f9bc863760448f14104cc8f42368.md b/docs/recommendations/5d150cec2775f9bc863760448f14104cc8f42368.md
index 50bb5b77..de2d866e 100644
--- a/docs/recommendations/5d150cec2775f9bc863760448f14104cc8f42368.md
+++ b/docs/recommendations/5d150cec2775f9bc863760448f14104cc8f42368.md
@@ -11,7 +11,7 @@ hide:
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-12-30 06:05:37 UTC</i>
+  <i class="footer">This page was last updated on 2025-01-06 06:05:56 UTC</i>
   </p>
   
   <div class="note info" onclick="startIntro()">
@@ -50,7 +50,7 @@ hide:
           </td>
           <td>2019-03-29</td>
           <td>Proceedings of the National Academy of Sciences of the United States of America</td>
-          <td>661</td>
+          <td>662</td>
           <td>68</td>
         </tr>
     
@@ -86,7 +86,7 @@ hide:
           </td>
           <td>2020-05-05</td>
           <td>Nature Communications</td>
-          <td>301</td>
+          <td>305</td>
           <td>13</td>
         </tr>
     
diff --git a/docs/recommendations/60d0d998fa038182b3b69a57adb9b2f82d40589c.md b/docs/recommendations/60d0d998fa038182b3b69a57adb9b2f82d40589c.md
index 33fa86b1..55c55e62 100644
--- a/docs/recommendations/60d0d998fa038182b3b69a57adb9b2f82d40589c.md
+++ b/docs/recommendations/60d0d998fa038182b3b69a57adb9b2f82d40589c.md
@@ -11,7 +11,7 @@ hide:
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-12-30 06:05:39 UTC</i>
+  <i class="footer">This page was last updated on 2025-01-06 06:05:56 UTC</i>
   </p>
   
   <div class="note info" onclick="startIntro()">
@@ -147,7 +147,7 @@ hide:
           </td>
           <td>2020-01-13</td>
           <td>ArXiv</td>
-          <td>516</td>
+          <td>517</td>
           <td>26</td>
         </tr>
     
diff --git a/docs/recommendations/648d90b713997a771e2c49f02cd771e8b7b10b37.md b/docs/recommendations/648d90b713997a771e2c49f02cd771e8b7b10b37.md
index e7457c7e..31fa43c0 100644
--- a/docs/recommendations/648d90b713997a771e2c49f02cd771e8b7b10b37.md
+++ b/docs/recommendations/648d90b713997a771e2c49f02cd771e8b7b10b37.md
@@ -11,7 +11,7 @@ hide:
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-12-30 06:05:26 UTC</i>
+  <i class="footer">This page was last updated on 2025-01-06 06:05:44 UTC</i>
   </p>
   
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@@ -110,7 +110,7 @@ hide:
           </td>
           <td>2023-10-21</td>
           <td>ArXiv</td>
-          <td>33</td>
+          <td>34</td>
           <td>4</td>
         </tr>
     
diff --git a/docs/recommendations/73dd9c49f205280991826b2ea4b50344203916b4.md b/docs/recommendations/73dd9c49f205280991826b2ea4b50344203916b4.md
index 23ef27a7..c0619f11 100644
--- a/docs/recommendations/73dd9c49f205280991826b2ea4b50344203916b4.md
+++ b/docs/recommendations/73dd9c49f205280991826b2ea4b50344203916b4.md
@@ -11,7 +11,7 @@ hide:
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-12-30 06:05:45 UTC</i>
+  <i class="footer">This page was last updated on 2025-01-06 06:05:59 UTC</i>
   </p>
   
   <div class="note info" onclick="startIntro()">
@@ -51,7 +51,7 @@ hide:
           <td>2022-09-04</td>
           <td>Scientific Reports</td>
           <td>4</td>
-          <td>24</td>
+          <td>25</td>
         </tr>
     
         <tr id="Data-driven modeling frameworks that adopt sparse regression techniques, such as sparse identification of nonlinear dynamics (SINDy) and its modifications, are developed to resolve difficulties in extracting underlying dynamics from experimental data. In contrast to neural-network-based methods, these methods are designed to obtain white-box analytical models. In this work, we incorporate the concept of SINDy and knowledge in the field of classical mechanics to identify interpretable and sparse expressions of total energy and the Lagrangian that shelters the hidden dynamics. Moreover, our method (hereafter referred as Lagrangian-SINDy) is developed to use knowledge of simple systems that form the system being analyzed to ensure the likelihood of correct results and to improve the learning pace. Lagrangian-SINDy is highly accurate in discovering interpretable dynamics via energy-related physical quantities. Its performance is validated with three popular multi-DOF nonlinear dynamical systems, namely the spherical pendulum, double pendulum and cart-pendulum system. Comparisons with other SINDy-based methods are made and Lagrangian-SINDy is found to provide the most compact analytical models.">
@@ -63,7 +63,7 @@ hide:
           <td>2020-01-31</td>
           <td>IEEE Robotics and Automation Letters</td>
           <td>24</td>
-          <td>24</td>
+          <td>25</td>
         </tr>
     
         <tr id="In this work we analyze the effectiveness of the Sparse Identification of Nonlinear Dynamics (SINDy) technique on three benchmark datasets for nonlinear identification, to provide a better understanding of its suitability when tackling real dynamical systems. While SINDy can be an appealing strategy for pursuing physics-based learning, our analysis highlights difficulties in dealing with unobserved states and non-smooth dynamics. Due to the ubiquity of these features in real systems in general, and control applications in particular, we complement our analysis with hands-on approaches to tackle these issues in order to exploit SINDy also in these challenging contexts.">
@@ -110,7 +110,7 @@ hide:
           </td>
           <td>2017-11-15</td>
           <td>Proceedings. Mathematical, Physical, and Engineering Sciences</td>
-          <td>470</td>
+          <td>472</td>
           <td>68</td>
         </tr>
     
@@ -134,20 +134,20 @@ hide:
           </td>
           <td>2020-04-05</td>
           <td>Proceedings. Mathematical, Physical, and Engineering Sciences</td>
-          <td>225</td>
+          <td>227</td>
           <td>68</td>
         </tr>
     
-        <tr id="Physics-based and first-principles models pervade the engineering and physical sciences, allowing for the ability to model the dynamics of complex systems with a prescribed accuracy. The approximations used in deriving governing equations often result in discrepancies between the model and sensor-based measurements of the system, revealing the approximate nature of the equations and/or the signal-to-noise ratio of the sensor itself. In modern dynamical systems, such discrepancies between model and measurement can lead to poor quantification, often undermining the ability to produce accurate and precise control algorithms. We introduce a discrepancy modeling framework to identify the missing physics and resolve the model-measurement mismatch with two distinct approaches: (i) by learning a model for the evolution of systematic state-space residual, and (ii) by discovering a model for the deterministic dynamical error. Regardless of approach, a common suite of data-driven model discovery methods can be used. The choice of method depends on one's intent (e.g., mechanistic interpretability) for discrepancy modeling, sensor measurement characteristics (e.g., quantity, quality, resolution), and constraints imposed by practical applications (e.g., modeling approaches using the suite of data-driven modeling methods on three continuous dynamical systems under varying signal-to-noise ratios. Finally, we emphasize structural shortcomings of each discrepancy modeling approach depending on error type. In summary, if the true dynamics are unknown (i.e., an imperfect model), one should learn a discrepancy model of the missing physics in the dynamical space. Yet, if the true dynamics are known yet model-measurement mismatch still exists, one should learn a discrepancy model in the state space.">
+        <tr id="We consider the problem of learning the dynamics of a linear system when one has access to data generated by an auxiliary system that shares similar (but not identical) dynamics, in addition to data from the true system. We use a weighted least squares approach, and provide finite sample error bounds of the learned model as a function of the number of samples and various system parameters from the two systems as well as the weight assigned to the auxiliary data. We show that the auxiliary data can help to reduce the intrinsic system identification error due to noise, at the price of adding a portion of error that is due to the differences between the two system models. We further provide a data-dependent bound that is computable when some prior knowledge about the systems, such as upper bounds on noise levels and model difference, is available. This bound can also be used to determine the weight that should be assigned to the auxiliary data during the model training stage.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/c4a38c94d23389326f5043d63b9f5f6f0d8c0c50" target='_blank'>Discrepancy Modeling Framework: Learning Missing Physics, Modeling Systematic Residuals, and Disambiguating between Deterministic and Random Effects</a></td>
+          <td><a href="https://www.semanticscholar.org/paper/f22b5a826ef61edb741f547b6e73999476cd695d" target='_blank'>Learning Dynamical Systems by Leveraging Data from Similar Systems</a></td>
           <td>
-            Megan R. Ebers, K. Steele, J. Kutz
+            Lei Xin, Lintao Ye, G. Chiu, S. Sundaram
           </td>
-          <td>2022-03-10</td>
-          <td>SIAM J. Appl. Dyn. Syst.</td>
-          <td>11</td>
-          <td>33</td>
+          <td>2023-02-08</td>
+          <td>ArXiv</td>
+          <td>7</td>
+          <td>37</td>
         </tr>
     
   </tbody>
diff --git a/docs/recommendations/883547fdbd88552328a6615ec620f96e39c57018.md b/docs/recommendations/883547fdbd88552328a6615ec620f96e39c57018.md
index a0f8c799..b0cbddea 100644
--- a/docs/recommendations/883547fdbd88552328a6615ec620f96e39c57018.md
+++ b/docs/recommendations/883547fdbd88552328a6615ec620f96e39c57018.md
@@ -11,7 +11,7 @@ hide:
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-12-30 06:05:47 UTC</i>
+  <i class="footer">This page was last updated on 2025-01-06 06:06:10 UTC</i>
   </p>
   
   <div class="note info" onclick="startIntro()">
@@ -98,7 +98,7 @@ hide:
           </td>
           <td>2020-04-05</td>
           <td>Proceedings. Mathematical, Physical, and Engineering Sciences</td>
-          <td>225</td>
+          <td>227</td>
           <td>68</td>
         </tr>
     
@@ -122,7 +122,7 @@ hide:
           </td>
           <td>2015-09-11</td>
           <td>Proceedings of the National Academy of Sciences</td>
-          <td>3476</td>
+          <td>3490</td>
           <td>68</td>
         </tr>
     
@@ -138,16 +138,16 @@ hide:
           <td>0</td>
         </tr>
     
-        <tr id="We consider the data-driven discovery of governing equations from time-series data in the limit of high noise. The algorithms developed describe an extensive toolkit of methods for circumventing the deleterious effects of noise in the context of the <italic>sparse identification of nonlinear dynamics</italic> (SINDy) framework. We offer two primary contributions, both focused on noisy data acquired from a system <inline-formula> <tex-math notation="LaTeX">$\dot { \boldsymbol x} = { \boldsymbol f} ({ \boldsymbol x})$ </tex-math></inline-formula>. First, we propose, for use in high-noise settings, an extensive toolkit of critically enabling extensions for the SINDy regression method, to progressively cull functionals from an over-complete library and yield a set of sparse equations that regress to the derivate <inline-formula> <tex-math notation="LaTeX">$\dot { \boldsymbol {x}}$ </tex-math></inline-formula>. This toolkit includes: (regression step) weight timepoints based on estimated noise, use ensembles to estimate coefficients, and regress using FFTs; (culling step) leverage linear dependence of functionals, and restore and protect culled functionals based on Figures of Merit (FoMs). In a novel Assessment step, we define FoMs that compare model predictions to the original time-series (i.e., <inline-formula> <tex-math notation="LaTeX">${ \boldsymbol x}(t)$ </tex-math></inline-formula> rather than <inline-formula> <tex-math notation="LaTeX">$\dot { \boldsymbol {x}}(t)$ </tex-math></inline-formula>). These innovations can extract sparse governing equations and coefficients from high-noise time-series data (e.g., 300% added noise). For example, it discovers the correct sparse libraries in the Lorenz system, with median coefficient estimate errors equal to 1%−3% (for 50% noise), 6%−8% (for 100% noise), and 23%−25% (for 300% noise). The enabling modules in the toolkit are combined into a single method, but the individual modules can be tactically applied in other equation discovery methods (SINDy or not) to improve results on high-noise data. Second, we propose a technique, applicable to any model discovery method based on <inline-formula> <tex-math notation="LaTeX">$\dot { \boldsymbol x} = { \boldsymbol f} ({ \boldsymbol x})$ </tex-math></inline-formula>, to assess the accuracy of a discovered model in the context of non-unique solutions due to noisy data. Currently, this non-uniqueness can obscure a discovered model’s accuracy and thus a discovery method’s effectiveness. We describe a technique that uses linear dependencies among functionals to transform a discovered model into an equivalent form that is closest to the <italic>true</italic> model, enabling more accurate assessment of a discovered model’s correctness.">
+        <tr id="Active learning algorithms strategically select informative input samples, aiming to enhance understanding and optimize sample efficiency for dynamical systems. The efficacy of machine learning (ML) models with uncertainty quantification in identifying dynamical systems with different characteristics has not yet been explored. This paper investigates four ML models: Gaussian processes (GPs) with radial basis function (RBF), GPs with Matérn kernels, Bayesian neural networks (NNs) with Monte Carlo dropout(MCD), and ensemble neural networks (ENNs). Both continuous and non-continuous learning strategies are employed for all models. Five well known dynamical systems with different characteristics, state dimensionalities, and dynamical complexities are simulated to test the performance of the models along the metrics of test RMSE as well as samples and run time until convergence. Through systematic experimentation, this paper provides guidance for researchers selecting models and algorithms in active learning for system identification, with insights into their strengths and limitations. Gaussian Processes with RBF kernels are shown to be the best overall choice while ENNs with Bayesian inference emerge as a scalable alternative, showing promise for high-dimensional tasks. Employing continuous training has proven to enhance the performance of Gaussian processes with RBF kernels, as well as ENNs, resulting in significant improvements in both sample and run-time efficiency.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/a9803137946f0dc8997f23de925d5aec6e92dfb9" target='_blank'>A Toolkit for Data-Driven Discovery of Governing Equations in High-Noise Regimes</a></td>
+          <td><a href="https://www.semanticscholar.org/paper/4a3887d48d70464cf825d7d6d8834e36e77b5d04" target='_blank'>Comparative Analysis of Uncertainty Quantification Models in Active Learning for Efficient System Identification of Dynamical Systems</a></td>
           <td>
-            Charles B. Delahunt, J. Kutz
+            Hans Mertens, Frances Zhu
           </td>
-          <td>2021-11-08</td>
-          <td>IEEE Access</td>
-          <td>18</td>
-          <td>33</td>
+          <td>2024-08-28</td>
+          <td>2024 IEEE 20th International Conference on Automation Science and Engineering (CASE)</td>
+          <td>0</td>
+          <td>0</td>
         </tr>
     
   </tbody>
diff --git a/docs/recommendations/b2eb064f432557c59ce99834d7dc7817e4687271.md b/docs/recommendations/b2eb064f432557c59ce99834d7dc7817e4687271.md
index fc779e2d..e831eeca 100644
--- a/docs/recommendations/b2eb064f432557c59ce99834d7dc7817e4687271.md
+++ b/docs/recommendations/b2eb064f432557c59ce99834d7dc7817e4687271.md
@@ -11,7 +11,7 @@ hide:
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-12-30 06:05:42 UTC</i>
+  <i class="footer">This page was last updated on 2025-01-06 06:05:58 UTC</i>
   </p>
   
   <div class="note info" onclick="startIntro()">
@@ -75,7 +75,7 @@ hide:
           <td>2020-01-31</td>
           <td>IEEE Robotics and Automation Letters</td>
           <td>24</td>
-          <td>24</td>
+          <td>25</td>
         </tr>
     
         <tr id="System identification, the process of deriving mathematical models of dynamical systems from observed input-output data, has undergone a paradigm shift with the advent of learning-based methods. Addressing the intricate challenges of data-driven discovery in nonlinear dynamical systems, these methods have garnered significant attention. Among them, Sparse Identification of Nonlinear Dynamics (SINDy) has emerged as a transformative approach, distilling complex dynamical behaviors into interpretable linear combinations of basis functions. However, SINDy relies on domain-specific expertise to construct its foundational"library"of basis functions, which limits its adaptability and universality. In this work, we introduce a nonlinear system identification framework called LeARN that transcends the need for prior domain knowledge by learning the library of basis functions directly from data. To enhance adaptability to evolving system dynamics under varying noise conditions, we employ a novel meta-learning-based system identification approach that uses a lightweight deep neural network (DNN) to dynamically refine these basis functions. This not only captures intricate system behaviors but also adapts seamlessly to new dynamical regimes. We validate our framework on the Neural Fly dataset, showcasing its robust adaptation and generalization capabilities. Despite its simplicity, our LeARN achieves competitive dynamical error performance compared to SINDy. This work presents a step toward the autonomous discovery of dynamical systems, paving the way for a future where machine learning uncovers the governing principles of complex systems without requiring extensive domain-specific interventions.">
@@ -98,7 +98,7 @@ hide:
           </td>
           <td>2020-04-05</td>
           <td>Proceedings. Mathematical, Physical, and Engineering Sciences</td>
-          <td>225</td>
+          <td>227</td>
           <td>68</td>
         </tr>
     
@@ -114,14 +114,14 @@ hide:
           <td>1</td>
         </tr>
     
-        <tr id="The sparse identification of nonlinear dynamics (SINDy) has been established as an effective technique to produce interpretable models of dynamical systems from time-resolved state data via sparse regression. However, to model parameterized systems, SINDy requires data from transient trajectories for various parameter values over the range of interest, which are typically difficult to acquire experimentally. In this work, we extend SINDy to be able to leverage data on fixed points and/or limit cycles to reduce the number of transient trajectories needed for successful system identification. To achieve this, we incorporate the data on these attractors at various parameter values as constraints in the optimization problem. First, we show that enforcing these as hard constraints leads to an ill-conditioned regression problem due to the large number of constraints. Instead, we implement soft constraints by modifying the cost function to be minimized. This leads to the formulation of a multi-objective sparse regression problem where we simultaneously seek to minimize the error of the fit to the transients trajectories and to the data on attractors, while penalizing the number of terms in the model. Our extension, demonstrated on several numerical examples, is more robust to noisy measurements and requires substantially less training data than the original SINDy method to correctly identify a parameterized dynamical system.">
+        <tr id="None">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
           <td><a href="https://www.semanticscholar.org/paper/0c03c126b4d641a81099470f03a7d5215a2a6820" target='_blank'>Multi-objective SINDy for parameterized model discovery from single transient trajectory data</a></td>
           <td>
             Javier A. Lemus, Benjamin Herrmann
           </td>
           <td>2024-05-14</td>
-          <td>ArXiv</td>
+          <td>Nonlinear Dynamics</td>
           <td>0</td>
           <td>0</td>
         </tr>
@@ -134,7 +134,7 @@ hide:
           </td>
           <td>2015-09-11</td>
           <td>Proceedings of the National Academy of Sciences</td>
-          <td>3476</td>
+          <td>3490</td>
           <td>68</td>
         </tr>
     
@@ -146,7 +146,7 @@ hide:
           </td>
           <td>2021-11-12</td>
           <td>J. Open Source Softw.</td>
-          <td>124</td>
+          <td>125</td>
           <td>68</td>
         </tr>
     
diff --git a/docs/recommendations/c0fc3882a9976f6a9cdc3a724bce184b786503da.md b/docs/recommendations/c0fc3882a9976f6a9cdc3a724bce184b786503da.md
index 2f3deb9f..953bfb9a 100644
--- a/docs/recommendations/c0fc3882a9976f6a9cdc3a724bce184b786503da.md
+++ b/docs/recommendations/c0fc3882a9976f6a9cdc3a724bce184b786503da.md
@@ -11,7 +11,7 @@ hide:
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-12-30 06:05:48 UTC</i>
+  <i class="footer">This page was last updated on 2025-01-06 06:06:16 UTC</i>
   </p>
   
   <div class="note info" onclick="startIntro()">
@@ -62,7 +62,7 @@ hide:
           </td>
           <td>2019-01-29</td>
           <td>ArXiv</td>
-          <td>48</td>
+          <td>49</td>
           <td>36</td>
         </tr>
     
diff --git a/docs/recommendations/c3c94ccc094dcf546e8e31c9a42506302e837524.md b/docs/recommendations/c3c94ccc094dcf546e8e31c9a42506302e837524.md
index 5094223d..9d3215a4 100644
--- a/docs/recommendations/c3c94ccc094dcf546e8e31c9a42506302e837524.md
+++ b/docs/recommendations/c3c94ccc094dcf546e8e31c9a42506302e837524.md
@@ -11,7 +11,7 @@ hide:
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-12-30 06:05:28 UTC</i>
+  <i class="footer">This page was last updated on 2025-01-06 06:05:45 UTC</i>
   </p>
   
   <div class="note info" onclick="startIntro()">
@@ -122,20 +122,20 @@ hide:
           </td>
           <td>2022-02-17</td>
           <td>IEEE Transactions on Knowledge and Data Engineering</td>
-          <td>78</td>
+          <td>79</td>
           <td>44</td>
         </tr>
     
-        <tr id="Existing multivariate time series anomaly detection methods utilize graph neural networks to model inter-sensor dependencies and achieve satisfactory results. However, these methods often employ a predefined or self-learning static adjacency matrix for graph information aggregation, disregarding the dynamic characteristics of inter-sensor dependencies in the real world, which change over time and are observable at different time scales as dynamic changing graph structure information. Furthermore, existing techniques struggle to capture long-term temporal contextual relationships. To address these issues, we propose a Dynamic Graph Learning with Long and Short-term time model (DGL-LS) for multivariate time series anomaly detection. The network integrates a dynamic graph structure learning method among sensors in multi-time mode and long- and short-term temporal context information to enhance the prediction of multivariate time series anomalies. We propose a strategy for learning dynamic graphs that aggregates sensor node representations at various time intervals, and then uses an attention-based gating unit to evolve the node dynamic characterization and construct a series of adjacency matrices that describe the dynamic changes in graph structure over time. Moreover, we formulate a long-short time convolution to capture the long-term and short-term temporal dependencies within the time series. We demonstrate the superiority of our approach over other state-of-the-art methods by conducting extensive experiments on three publicly available datasets.">
+        <tr id="The online prediction of multivariate signals, existing simultaneously in space and time, from noisy partial observations is a fundamental task in numerous applications. We propose an efficient Neural Network architecture for the online estimation of time-varying graph signals named the Adaptive Least Mean Squares Graph Neural Networks (LMS-GNN). LMS-GNN aims to capture the time variation and bridge the cross-space-time interactions under the condition that signals are corrupted by noise and missing values. The LMS-GNN is a combination of adaptive graph filters and Graph Neural Networks (GNN). At each time step, the forward propagation of LMS-GNN is similar to adaptive graph filters where the output is based on the error between the observation and the prediction similar to GNN. The filter coefficients are updated via backpropagation as in GNN. Experimenting on real-world temperature data reveals that our LMS-GNN achieves more accurate online predictions compared to graph-based methods like adaptive graph filters and graph convolutional neural networks.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/379f54e4519d51a31de25e26fa651b3bd21d6530" target='_blank'>Dynamic Graph Learning with Long and Short-Term for Multivariate Time Series Anomaly Detection</a></td>
+          <td><a href="https://www.semanticscholar.org/paper/a03d0f3fd814c3732704bc65e2e60d0a92b0e8ae" target='_blank'>Adaptive Least Mean Squares Graph Neural Networks and Online Graph Signal Estimation</a></td>
           <td>
-            Yuyin Tian, Rong Gao, Lingyu Yan, Donghua Liu, Zhiwei Ye
+            Yi Yan, Changran Peng, E. Kuruoglu
           </td>
-          <td>2023-09-07</td>
-          <td>2023 IEEE 12th International Conference on Intelligent Data Acquisition and Advanced Computing Systems: Technology and Applications (IDAACS)</td>
-          <td>0</td>
-          <td>4</td>
+          <td>2024-01-27</td>
+          <td>ArXiv</td>
+          <td>1</td>
+          <td>26</td>
         </tr>
     
   </tbody>
diff --git a/docs/recommendations/ccea298edb788edf821aef58f0952c3e8debc25a.md b/docs/recommendations/ccea298edb788edf821aef58f0952c3e8debc25a.md
index 2ef56337..4a6c8d3c 100644
--- a/docs/recommendations/ccea298edb788edf821aef58f0952c3e8debc25a.md
+++ b/docs/recommendations/ccea298edb788edf821aef58f0952c3e8debc25a.md
@@ -11,7 +11,7 @@ hide:
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-12-30 06:05:19 UTC</i>
+  <i class="footer">This page was last updated on 2025-01-06 06:05:39 UTC</i>
   </p>
   
   <div class="note info" onclick="startIntro()">
@@ -98,7 +98,7 @@ hide:
           </td>
           <td>2020-05-24</td>
           <td>Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining</td>
-          <td>1142</td>
+          <td>1149</td>
           <td>57</td>
         </tr>
     
diff --git a/docs/recommendations/d3dbbd0f0de51b421a6220bd6480b8d2e99a88e9.md b/docs/recommendations/d3dbbd0f0de51b421a6220bd6480b8d2e99a88e9.md
index fc975d04..1ce08662 100644
--- a/docs/recommendations/d3dbbd0f0de51b421a6220bd6480b8d2e99a88e9.md
+++ b/docs/recommendations/d3dbbd0f0de51b421a6220bd6480b8d2e99a88e9.md
@@ -11,7 +11,7 @@ hide:
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-12-30 06:05:16 UTC</i>
+  <i class="footer">This page was last updated on 2025-01-06 06:05:37 UTC</i>
   </p>
   
   <div class="note info" onclick="startIntro()">
diff --git a/docs/recommendations/e2a83369383aff37224170c1ae3d3870d5d9e419.md b/docs/recommendations/e2a83369383aff37224170c1ae3d3870d5d9e419.md
index d8fad9b1..21657999 100644
--- a/docs/recommendations/e2a83369383aff37224170c1ae3d3870d5d9e419.md
+++ b/docs/recommendations/e2a83369383aff37224170c1ae3d3870d5d9e419.md
@@ -11,7 +11,7 @@ hide:
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-12-30 06:05:18 UTC</i>
+  <i class="footer">This page was last updated on 2025-01-06 06:05:38 UTC</i>
   </p>
   
   <div class="note info" onclick="startIntro()">
diff --git a/docs/recommendations/e2e1f1b8e6c1b7f4f166e15b7c674945856a51b6.md b/docs/recommendations/e2e1f1b8e6c1b7f4f166e15b7c674945856a51b6.md
index f3819a9e..f543e41b 100644
--- a/docs/recommendations/e2e1f1b8e6c1b7f4f166e15b7c674945856a51b6.md
+++ b/docs/recommendations/e2e1f1b8e6c1b7f4f166e15b7c674945856a51b6.md
@@ -11,7 +11,7 @@ hide:
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-12-30 06:05:25 UTC</i>
+  <i class="footer">This page was last updated on 2025-01-06 06:05:43 UTC</i>
   </p>
   
   <div class="note info" onclick="startIntro()">
@@ -110,7 +110,7 @@ hide:
           </td>
           <td>2024-03-12</td>
           <td>ArXiv</td>
-          <td>82</td>
+          <td>85</td>
           <td>18</td>
         </tr>
     
@@ -134,7 +134,7 @@ hide:
           </td>
           <td>2024-05-03</td>
           <td>ArXiv</td>
-          <td>13</td>
+          <td>14</td>
           <td>47</td>
         </tr>
     
diff --git a/docs/recommendations/e6f0a85009481dcfd93aaa43ed3f980e5033b0d8.md b/docs/recommendations/e6f0a85009481dcfd93aaa43ed3f980e5033b0d8.md
index b903db39..6f16a149 100644
--- a/docs/recommendations/e6f0a85009481dcfd93aaa43ed3f980e5033b0d8.md
+++ b/docs/recommendations/e6f0a85009481dcfd93aaa43ed3f980e5033b0d8.md
@@ -11,7 +11,7 @@ hide:
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-12-30 06:05:47 UTC</i>
+  <i class="footer">This page was last updated on 2025-01-06 06:06:11 UTC</i>
   </p>
   
   <div class="note info" onclick="startIntro()">
@@ -62,7 +62,7 @@ hide:
           </td>
           <td>2015-09-11</td>
           <td>Proceedings of the National Academy of Sciences</td>
-          <td>3476</td>
+          <td>3490</td>
           <td>68</td>
         </tr>
     
@@ -86,7 +86,7 @@ hide:
           </td>
           <td>2021-11-12</td>
           <td>J. Open Source Softw.</td>
-          <td>124</td>
+          <td>125</td>
           <td>68</td>
         </tr>
     
@@ -110,7 +110,7 @@ hide:
           </td>
           <td>2020-05-05</td>
           <td>Nature Communications</td>
-          <td>301</td>
+          <td>305</td>
           <td>13</td>
         </tr>
     
@@ -135,7 +135,7 @@ hide:
           <td>2020-01-31</td>
           <td>IEEE Robotics and Automation Letters</td>
           <td>24</td>
-          <td>24</td>
+          <td>25</td>
         </tr>
     
         <tr id="Many dynamical systems of interest are nonlinear, with examples in turbulence, epidemiology, neuroscience, and finance, making them difficult to control using linear approaches. Model predictive control (MPC) is a powerful model-based optimization technique that enables the control of such nonlinear systems with constraints. However, modern systems often lack computationally tractable models, motivating the use of system identification techniques to learn accurate and efficient models for real-time control. In this tutorial article, we review emerging data-driven methods for model discovery and how they are used for nonlinear MPC. In particular, we focus on the sparse identification of nonlinear dynamics (SINDy) algorithm and show how it may be used with MPC on an infectious disease control example. We compare the performance against MPC based on a linear dynamic mode decomposition (DMD) model. Code is provided to run the tutorial examples and may be modified to extend this data-driven control framework to arbitrary nonlinear systems.">
diff --git a/docs/recommendations/f45f85fa1beaa795c24c4ff86f1f2deece72252f.md b/docs/recommendations/f45f85fa1beaa795c24c4ff86f1f2deece72252f.md
index 9537e1e8..b71ef3b1 100644
--- a/docs/recommendations/f45f85fa1beaa795c24c4ff86f1f2deece72252f.md
+++ b/docs/recommendations/f45f85fa1beaa795c24c4ff86f1f2deece72252f.md
@@ -11,7 +11,7 @@ hide:
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-12-30 06:05:22 UTC</i>
+  <i class="footer">This page was last updated on 2025-01-06 06:05:41 UTC</i>
   </p>
   
   <div class="note info" onclick="startIntro()">
@@ -98,7 +98,7 @@ hide:
           </td>
           <td>2023-10-03</td>
           <td>ArXiv</td>
-          <td>213</td>
+          <td>214</td>
           <td>9</td>
         </tr>
     
diff --git a/docs/recommendations/ff1f1cf9df8c413ec7345da7604ba28597da5b90.md b/docs/recommendations/ff1f1cf9df8c413ec7345da7604ba28597da5b90.md
index 5dd8e918..df2135ec 100644
--- a/docs/recommendations/ff1f1cf9df8c413ec7345da7604ba28597da5b90.md
+++ b/docs/recommendations/ff1f1cf9df8c413ec7345da7604ba28597da5b90.md
@@ -11,7 +11,7 @@ hide:
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-12-30 06:05:29 UTC</i>
+  <i class="footer">This page was last updated on 2025-01-06 06:05:46 UTC</i>
   </p>
   
   <div class="note info" onclick="startIntro()">
@@ -49,7 +49,7 @@ hide:
             Yong Liu, Haoran Zhang, Chenyu Li, Xiangdong Huang, Jianmin Wang, Mingsheng Long
           </td>
           <td>2024-02-04</td>
-          <td>ArXiv, DBLP</td>
+          <td>DBLP, ArXiv</td>
           <td>26</td>
           <td>67</td>
         </tr>
@@ -78,7 +78,7 @@ hide:
           <td>67</td>
         </tr>
     
-        <tr id="The field of general time series analysis has recently begun to explore unified modeling, where a common architectural backbone can be retrained on a specific task for a specific dataset. In this work, we approach unification from a complementary vantage point: unification across tasks and domains. To this end, we explore the impact of discrete, learnt, time series data representations that enable generalist, cross-domain training. Our method, TOTEM, or TOkenized Time Series EMbeddings, proposes a simple tokenizer architecture that embeds time series data from varying domains using a discrete vectorized representation learned in a self-supervised manner. TOTEM works across multiple tasks and domains with minimal to no tuning. We study the efficacy of TOTEM with an extensive evaluation on 17 real world time series datasets across 3 tasks. We evaluate both the specialist (i.e., training a model on each domain) and generalist (i.e., training a single model on many domains) settings, and show that TOTEM matches or outperforms previous best methods on several popular benchmarks. The code can be found at: https://github.com/SaberaTalukder/TOTEM.">
+        <tr id="This work studies the problem of time series analysis with generalist (or foundation) models, which are models trained across many data domains. Drawing inspiration from the widespread success of large language models, we consider the simple strategy of discretely tokenizing time series data drawn from a myriad of datasets via self-supervision, then using the fixed tokenization to solve a variety of tasks across many data domains. Canonically, time series models are either trained on a single dataset or built in a task-specific manner (e.g., a forecasting-only model), where many use patches of time as inputs to the model. As such, performant generalist, discrete representation time series models explored across many tasks are of value. Our method, TOkenized Time Series EMbeddings (TOTEM), produces such generalist time series models with minimal or no fine-tuning while exhibiting strong zero-shot performance. We evaluate TOTEM extensively over nearly 500 experiments on three commonly-studied time series tasks with real-world data: imputation (17 baselines, 12 datasets), anomaly detection (19 baselines, 25 datasets), and forecasting (14 baselines, 12 datasets). We conclude that TOTEM matches or outperforms existing state-of-the-art models in both the canonical specialist setting (i.e., training one model on one domain) as well as the generalist setting (i.e., training a single model on many domains), which demonstrates the efficacy of tokenization for general time series analysis. The open-source implementation is available here: https://github.com/SaberaTalukder/TOTEM; a video summary is available here: https://www.youtube.com/watch?v=OqrCpdb6MJk.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
           <td><a href="https://www.semanticscholar.org/paper/f9f09c782155ca4f2ae4b6ffcf28514b439226cd" target='_blank'>TOTEM: TOkenized Time Series EMbeddings for General Time Series Analysis</a></td>
           <td>
@@ -98,7 +98,7 @@ hide:
           </td>
           <td>2024-01-08</td>
           <td>ArXiv</td>
-          <td>6</td>
+          <td>7</td>
           <td>7</td>
         </tr>
     
@@ -110,7 +110,7 @@ hide:
           </td>
           <td>2024-03-12</td>
           <td>ArXiv</td>
-          <td>82</td>
+          <td>85</td>
           <td>18</td>
         </tr>
     
diff --git a/site/Symbolic regression/index.html b/site/Symbolic regression/index.html
index cf2b0237..823d819d 100644
--- a/site/Symbolic regression/index.html	
+++ b/site/Symbolic regression/index.html	
@@ -451,7 +451,7 @@ <h1>Symbolic regression</h1>
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-12-30 06:05:56 UTC</i>
+  <i class="footer">This page was last updated on 2025-01-06 06:06:23 UTC</i>
   </p>
 
   <div class="note info" onclick="startIntro()">
@@ -515,8 +515,8 @@ <h3 id="manually_curated_articles">Manually curated articles on <i>Symbolic regr
             S. Brunton, J. Proctor, J. Kutz
           </td>
           <td>2015-09-11</td>
-          <td>Proceedings of the National Academy of Sciences, Proceedings of the National Academy of Sciences of the United States of America</td>
-          <td>3476</td>
+          <td>Proceedings of the National Academy of Sciences of the United States of America, Proceedings of the National Academy of Sciences</td>
+          <td>3490</td>
           <td>68</td>
 
             <td><a href='../recommendations/5d150cec2775f9bc863760448f14104cc8f42368' target='_blank'>
@@ -536,7 +536,7 @@ <h3 id="manually_curated_articles">Manually curated articles on <i>Symbolic regr
           </td>
           <td>2021-02-24</td>
           <td>Nature Communications</td>
-          <td>92</td>
+          <td>93</td>
           <td>24</td>
 
             <td><a href='../recommendations/60d0d998fa038182b3b69a57adb9b2f82d40589c' target='_blank'>
@@ -556,7 +556,7 @@ <h3 id="manually_curated_articles">Manually curated articles on <i>Symbolic regr
           </td>
           <td>2019-03-29</td>
           <td>Proceedings of the National Academy of Sciences of the United States of America</td>
-          <td>661</td>
+          <td>662</td>
           <td>68</td>
 
             <td><a href='../recommendations/3c9961153493370500020c81527b3548c96f81e0' target='_blank'>
@@ -596,7 +596,7 @@ <h3 id="manually_curated_articles">Manually curated articles on <i>Symbolic regr
           </td>
           <td>2017-11-15</td>
           <td>Proceedings. Mathematical, Physical, and Engineering Sciences, Proceedings of the Royal Society A</td>
-          <td>470</td>
+          <td>472</td>
           <td>68</td>
 
             <td><a href='../recommendations/b2eb064f432557c59ce99834d7dc7817e4687271' target='_blank'>
@@ -615,8 +615,8 @@ <h3 id="manually_curated_articles">Manually curated articles on <i>Symbolic regr
             N. Mangan, S. Brunton, J. Proctor, J. Kutz
           </td>
           <td>2016-05-26</td>
-          <td>IEEE Transactions on Molecular, Biological and Multi-Scale Communications, IEEE Transactions on Molecular Biological and Multi-Scale Communications</td>
-          <td>339</td>
+          <td>IEEE Transactions on Molecular Biological and Multi-Scale Communications, IEEE Transactions on Molecular, Biological and Multi-Scale Communications</td>
+          <td>338</td>
           <td>68</td>
 
             <td><a href='../recommendations/06a0ba437d41a7c82c08a9636a4438c1b5031378' target='_blank'>
@@ -636,7 +636,7 @@ <h3 id="manually_curated_articles">Manually curated articles on <i>Symbolic regr
           </td>
           <td>2020-04-05</td>
           <td>Proceedings. Mathematical, Physical, and Engineering Sciences, Proceedings of the Royal Society A</td>
-          <td>225</td>
+          <td>227</td>
           <td>68</td>
 
             <td><a href='../recommendations/4971f9abd024e40fbbdff2e9492745b68a6bca01' target='_blank'>
@@ -675,7 +675,7 @@ <h3 id="manually_curated_articles">Manually curated articles on <i>Symbolic regr
             Kadierdan Kaheman, E. Kaiser, B. Strom, J. Kutz, S. Brunton
           </td>
           <td>2019-09-18</td>
-          <td>ArXiv, arXiv.org</td>
+          <td>arXiv.org, ArXiv</td>
           <td>36</td>
           <td>68</td>
 
@@ -696,7 +696,7 @@ <h3 id="manually_curated_articles">Manually curated articles on <i>Symbolic regr
           </td>
           <td>2019-06-19</td>
           <td>Frontiers in Artificial Intelligence</td>
-          <td>78</td>
+          <td>79</td>
           <td>68</td>
 
             <td><a href='../recommendations/35e2571c17246577e0bc1b9de57a314c3b60e220' target='_blank'>
@@ -716,7 +716,7 @@ <h3 id="manually_curated_articles">Manually curated articles on <i>Symbolic regr
           </td>
           <td>2016-09-21</td>
           <td>Science Advances</td>
-          <td>1252</td>
+          <td>1258</td>
           <td>68</td>
 
             <td><a href='../recommendations/0acd117521ef5aafb09fed02ab415523b330b058' target='_blank'>
@@ -736,7 +736,7 @@ <h3 id="manually_curated_articles">Manually curated articles on <i>Symbolic regr
           </td>
           <td>2021-11-22</td>
           <td>Proceedings. Mathematical, Physical, and Engineering Sciences, Proceedings of the Royal Society A</td>
-          <td>186</td>
+          <td>187</td>
           <td>68</td>
 
             <td><a href='../recommendations/883547fdbd88552328a6615ec620f96e39c57018' target='_blank'>
@@ -756,7 +756,7 @@ <h3 id="manually_curated_articles">Manually curated articles on <i>Symbolic regr
           </td>
           <td>2022-06-01</td>
           <td>Nonlinear Dynamics</td>
-          <td>31</td>
+          <td>32</td>
           <td>93</td>
 
             <td><a href='../recommendations/e6f0a85009481dcfd93aaa43ed3f980e5033b0d8' target='_blank'>
@@ -820,34 +820,19 @@ <h3 id="recommended_articles">Recommended articles on <i>Symbolic regression</i>
     </thead>
     <tbody>
 
-        <tr id="Sparse Identification of Nonlinear Dynamical Systems (SINDy) is a powerful tool for the data-driven discovery of governing equations. However, it encounters challenges when modeling complex dynamical systems involving high-order derivatives or discontinuities, particularly in the presence of noise. These limitations restrict its applicability across various fields in applied mathematics and physics. To mitigate these, we propose Laplace-Enhanced SparSe Identification of Nonlinear Dynamical Systems (LES-SINDy). By transforming time-series measurements from the time domain to the Laplace domain using the Laplace transform and integration by parts, LES-SINDy enables more accurate approximations of derivatives and discontinuous terms. It also effectively handles unbounded growth functions and accumulated numerical errors in the Laplace domain, thereby overcoming challenges in the identification process. The model evaluation process selects the most accurate and parsimonious dynamical systems from multiple candidates. Experimental results across diverse ordinary and partial differential equations show that LES-SINDy achieves superior robustness, accuracy, and parsimony compared to existing methods.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/cc9d7f1e9a7f7b37237e52d46d21299f816a377c" target='_blank'>
-              LES-SINDy: Laplace-Enhanced Sparse Identification of Nonlinear Dynamical Systems
-              </a>
-            </td>
-          <td>
-            Haoyang Zheng, Guang Lin
-          </td>
-          <td>2024-11-04</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>1</td>
-        </tr>
-
-        <tr id="Effectively controlling systems governed by Partial Differential Equations (PDEs) is crucial in several fields of Applied Sciences and Engineering. These systems usually yield significant challenges to conventional control schemes due to their nonlinear dynamics, partial observability, high-dimensionality once discretized, distributed nature, and the requirement for low-latency feedback control. Reinforcement Learning (RL), particularly Deep RL (DRL), has recently emerged as a promising control paradigm for such systems, demonstrating exceptional capabilities in managing high-dimensional, nonlinear dynamics. However, DRL faces challenges including sample inefficiency, robustness issues, and an overall lack of interpretability. To address these issues, we propose a data-efficient, interpretable, and scalable Dyna-style Model-Based RL framework for PDE control, combining the Sparse Identification of Nonlinear Dynamics with Control (SINDy-C) algorithm and an autoencoder (AE) framework for the sake of dimensionality reduction of PDE states and actions. This novel approach enables fast rollouts, reducing the need for extensive environment interactions, and provides an interpretable latent space representation of the PDE forward dynamics. We validate our method on two PDE problems describing fluid flows - namely, the 1D Burgers equation and 2D Navier-Stokes equations - comparing it against a model-free baseline, and carrying out an extensive analysis of the learned dynamics.">
+        <tr id="The multiscale and turbulent nature of Earth's atmosphere has historically rendered accurate weather modeling a hard problem. Recently, there has been an explosion of interest surrounding data-driven approaches to weather modeling, which in many cases show improved forecasting accuracy and computational efficiency when compared to traditional methods. However, many of the current data-driven approaches employ highly parameterized neural networks, often resulting in uninterpretable models and limited gains in scientific understanding. In this work, we address the interpretability problem by explicitly discovering partial differential equations governing various weather phenomena, identifying symbolic mathematical models with direct physical interpretations. The purpose of this paper is to demonstrate that, in particular, the Weak form Sparse Identification of Nonlinear Dynamics (WSINDy) algorithm can learn effective weather models from both simulated and assimilated data. Our approach adapts the standard WSINDy algorithm to work with high-dimensional fluid data of arbitrary spatial dimension. Moreover, we develop an approach for handling terms that are not integrable-by-parts, such as advection operators.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/c4afec07162a7a857a1ad05397d56c6a677f4b00" target='_blank'>
-              Interpretable and Efficient Data-driven Discovery and Control of Distributed Systems
+          <td><a href="https://www.semanticscholar.org/paper/c28108ddd9f02b1ab9c1acff283613e0c44f3699" target='_blank'>
+              Learning Weather Models from Data with WSINDy
               </a>
             </td>
           <td>
-            Florian Wolf, Nicolò Botteghi, Urban Fasel, Andrea Manzoni
+            Seth Minor, D. Messenger, Vanja Dukic, David M. Bortz
           </td>
-          <td>2024-11-06</td>
+          <td>2025-01-01</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>11</td>
+          <td>8</td>
         </tr>
 
         <tr id="The identification of governing equations for dynamical systems is an everlasting challenge for the fundamental research in science and engineering. Machine learning has exhibited great success in learn and predicting dynamical systems from data. However, the fundamental challenges still exist: discovering the exact governing equations from highly noisy data. In the present work, we propose a compressive sensing‐assisted mixed integer optimization (CS‐MIO) method to make a step forward from a modern discrete optimization lens. In particular, we first formulate the problem into a mixed integer optimization model. The discrete optimization nature of the model leads to exact variable selection by means of cardinality constraint, and thereby powerful capability of exact discovery of governing equations from noisy data. Such capability is further enhanced by incorporating compressive sensing and regularization techniques for highly noisy data and high‐dimensional problems. The case studies on classical dynamical systems have shown that CS‐MIO can discover the exact governing equations from large‐noise data, with up to two orders of magnitude larger noise compared with state‐of‐the‐art methods. We also show its effectiveness for high‐dimensional dynamical system identification through the chaotic Lorenz 96 system.">
@@ -865,21 +850,6 @@ <h3 id="recommended_articles">Recommended articles on <i>Symbolic regression</i>
           <td>1</td>
         </tr>
 
-        <tr id="Dynamical systems theory has long provided a foundation for understanding evolving phenomena across scientific domains. Yet, the application of this theory to complex real-world systems remains challenging due to issues in mathematical modeling, nonlinearity, and high dimensionality. In this work, we introduce a data-driven computational framework to derive low-dimensional linear models for nonlinear dynamical systems directly from raw experimental data. This framework enables global stability analysis through interpretable linear models that capture the underlying system structure. Our approach employs time-delay embedding, physics-informed deep autoencoders, and annealing-based regularization to identify novel low-dimensional coordinate representations, unlocking insights across a variety of simulated and previously unstudied experimental dynamical systems. These new coordinate representations enable accurate long-horizon predictions and automatic identification of intricate invariant sets while providing empirical stability guarantees. Our method offers a promising pathway to analyze complex dynamical behaviors across fields such as physics, climate science, and engineering, with broad implications for understanding nonlinear systems in the real world.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/ac835425463bfb6a585132a06ba8fbce9643ce8d" target='_blank'>
-              Automated Global Analysis of Experimental Dynamics through Low-Dimensional Linear Embeddings
-              </a>
-            </td>
-          <td>
-            Samuel A. Moore, Brian P. Mann, Boyuan Chen
-          </td>
-          <td>2024-11-01</td>
-          <td>ArXiv</td>
-          <td>1</td>
-          <td>2</td>
-        </tr>
-
         <tr id="Mathematical modeling is a powerful tool for describing, predicting, and understanding complex phenomena exhibited by real-world systems. However, identifying the equations that govern a system's dynamics from experimental data remains a significant challenge without a definitive solution. In this study, evolutionary computing techniques are presented to estimate the governing equations of a dynamical system using time-series data. The main approach is to propose polynomial equations with unknown coefficients, and subsequently perform a parametric estimation using genetic algorithms. Some of the main contributions of the present study are an adequate modification of the genetic algorithm to remove terms with minimal contributions, and a mechanism to escape local optima during the search. To evaluate the proposed method, we applied it to three dynamical systems: a linear model, a nonlinear model, and the Lorenz system. Our results demonstrate a reconstruction with an Integral Square Error below 0.22 and a coefficient of determination R-squared of 0.99 for all systems, indicating successful reconstruction of the governing dynamic equations.">
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           <td><a href="https://www.semanticscholar.org/paper/e69e512559ec02858a243472cd4d184f5b4feb24" target='_blank'>
@@ -910,21 +880,6 @@ <h3 id="recommended_articles">Recommended articles on <i>Symbolic regression</i>
           <td>4</td>
         </tr>
 
-        <tr id="We propose the use of the Extended Kalman Filter (EKF) for online data assimilation and update of a dynamic model, preliminary identified through the Sparse Identification of Nonlinear Dynamics (SINDy). This data-driven technique may avoid biases due to incorrect modelling assumptions and exploits SINDy to approximate the system dynamics leveraging a predefined library of functions, where active terms are selected and weighted by a sparse set of coefficients. This results in a physically-sound and interpretable dynamic model allowing to reduce epistemic uncertainty often affecting machine learning approaches. Treating the SINDy model coefficients as random variables, we propose to update them while acquiring (possibly noisy) system measurements, thus enabling the online identification of time-varying systems. These changes can stem from, e.g., varying operational conditions or unforeseen events. The EKF performs model adaptation through joint state-parameters estimation, with the Jacobian matrices required to computed the model sensitivity inexpensively evaluated from the SINDy model formulation. The effectiveness of this approach is demonstrated through three case studies: (i) a Lokta-Volterra model in which all parameters simultaneously evolve during the observation period; (ii) a Selkov model where the system undergoes a bifurcation not seen during the SINDy training; (iii) a MEMS arch exhibiting a 1:2 internal resonance. The ability of EKF of recovering inactivated functional terms from the SINDy library, or discarding unnecessary contribution, is also highlighted. Based on the presented applications, this method shows strong promise for handling time-varying nonlinear dynamic systems possibly experiencing bifurcating behaviours.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/2d108c654cd0caef592cad2586543c394a27e334" target='_blank'>
-              Online learning in bifurcating dynamic systems via SINDy and Kalman filtering
-              </a>
-            </td>
-          <td>
-            Luca Rosafalco, Paolo Conti, Andrea Manzoni, Stefano Mariani, A. Frangi
-          </td>
-          <td>2024-11-07</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>8</td>
-        </tr>
-
         <tr id="This work explores the relationship between state space methods and Koopman operator-based methods for predicting the time-evolution of nonlinear dynamical systems. We demonstrate that extended dynamic mode decomposition with dictionary learning (EDMD-DL), when combined with a state space projection, is equivalent to a neural network representation of the nonlinear discrete-time flow map on the state space. We highlight how this projection step introduces nonlinearity into the evolution equations, enabling significantly improved EDMD-DL predictions. With this projection, EDMD-DL leads to a nonlinear dynamical system on the state space, which can be represented in either discrete or continuous time. This system has a natural structure for neural networks, where the state is first expanded into a high dimensional feature space followed by a linear mapping which represents the discrete-time map or the vector field as a linear combination of these features. Inspired by these observations, we implement several variations of neural ordinary differential equations (ODEs) and EDMD-DL, developed by combining different aspects of their respective model structures and training procedures. We evaluate these methods using numerical experiments on chaotic dynamics in the Lorenz system and a nine-mode model of turbulent shear flow, showing comparable performance across methods in terms of short-time trajectory prediction, reconstruction of long-time statistics, and prediction of rare events. We also show that these methods provide comparable performance to a non-Markovian approach in terms of prediction of extreme events.">
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           <td><a href="https://www.semanticscholar.org/paper/8cc75f4d56d343c523e54f056068099875c37a6d" target='_blank'>
@@ -967,7 +922,7 @@ <h3 id="recommended_articles">Recommended articles on <i>Symbolic regression</i>
           <td>2024-12-01</td>
           <td>Entropy</td>
           <td>0</td>
-          <td>0</td>
+          <td>3</td>
         </tr>
 
         <tr id="Discovering governing equations of complex network dynamics is a fundamental challenge in contemporary science with rich data, which can uncover the mysterious patterns and mechanisms of the formation and evolution of complex phenomena in various fields and assist in decision-making. In this work, we develop a universal computational tool that can automatically, efficiently, and accurately learn the symbolic changing patterns of complex system states by combining the excellent fitting ability from deep learning and the equation inference ability from pre-trained symbolic regression. We conduct intensive experimental verifications on more than ten representative scenarios from physics, biochemistry, ecology, epidemiology, etc. Results demonstrate the outstanding effectiveness and efficiency of our tool by comparing with the state-of-the-art symbolic regression techniques for network dynamics. The application to real-world systems including global epidemic transmission and pedestrian movements has verified its practical applicability. We believe that our tool can serve as a universal solution to dispel the fog of hidden mechanisms of changes in complex phenomena, advance toward interpretability, and inspire more scientific discoveries.">
@@ -1045,64 +1000,64 @@ <h3 id="recommended_articles">Recommended articles on <i>Symbolic regression</i>
           <td>0</td>
         </tr>
 
-        <tr id="In complex physical systems, conventional differential equations often fall short in capturing non-local and memory effects, as they are limited to local dynamics and integer-order interactions. This study introduces a stepwise data-driven framework for discovering fractional differential equations (FDEs) directly from data. FDEs, known for their capacity to model non-local dynamics with fewer parameters than integer-order derivatives, can represent complex systems with long-range interactions. Our framework applies deep neural networks as surrogate models for denoising and reconstructing sparse and noisy observations while using Gaussian-Jacobi quadrature to handle the challenges posed by singularities in fractional derivatives. To optimize both the sparse coefficients and fractional order, we employ an alternating optimization approach that combines sparse regression with global optimization techniques. We validate the framework across various datasets, including synthetic anomalous diffusion data, experimental data on the creep behavior of frozen soils, and single-particle trajectories modeled by L\'{e}vy motion. Results demonstrate the framework's robustness in identifying the structure of FDEs across diverse noise levels and its capacity to capture integer-order dynamics, offering a flexible approach for modeling memory effects in complex systems.">
+        <tr id="Modal analysis has long been consolidated as a basic tool to interpret dynamics and build low-order models of mechanical, thermal, and fluid systems. Eigenmodes arising from the spectral decomposition of the underlying linearized dynamics represent spatial patterns in vibration, temperature, or velocity fields associated with simple time dynamics. However, for systems that depend on one or more parameters, eigenmodes obtained for one set of parameter values are not necessarily dynamically relevant in other regions of parameter space. In this work, we formulate a method to obtain an optimal orthogonal basis of eigen-deformation modes (EDMs) that capture eigenmode variations across a range of parameter values. Through numerical examples of common parameterized dynamical systems in engineering, we show that EDMs are useful for parameterized model reduction and to provide physical insight into the effects of parameter changes on the underlying dynamics.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/ea19e187b5ce3208f332cc671f31694cb533a2f6" target='_blank'>
-              A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems
+          <td><a href="https://www.semanticscholar.org/paper/6c99559695549bb72301b118424e8de590b3b645" target='_blank'>
+              Interpretable low-order representation of eigenmode deformation in parameterized dynamical systems
               </a>
             </td>
           <td>
-            Xiangnan Yu, Hao Xu, Zhiping Mao, Hongguang Sun, Yong Zhang, Dong-juan Zhang, Yuntian Chen
+            Nicolas Torres-Ulloa, Erick Kracht, Urban Fasel, Benjamin Herrmann
           </td>
-          <td>2024-12-05</td>
+          <td>2024-12-16</td>
           <td>ArXiv</td>
           <td>0</td>
           <td>11</td>
         </tr>
 
-        <tr id="Nonlinear optimal control is vital for numerous applications but remains challenging for unknown systems due to the difficulties in accurately modelling dynamics and handling computational demands, particularly in high-dimensional settings. This work develops a theoretically certifiable framework that integrates a modified Koopman operator approach with model-based reinforcement learning to address these challenges. By relaxing the requirements on observable functions, our method incorporates nonlinear terms involving both states and control inputs, significantly enhancing system identification accuracy. Moreover, by leveraging the power of neural networks to solve partial differential equations (PDEs), our approach is able to achieving stabilizing control for high-dimensional dynamical systems, up to 9-dimensional. The learned value function and control laws are proven to converge to those of the true system at each iteration. Additionally, the accumulated cost of the learned control closely approximates that of the true system, with errors ranging from $10^{-5}$ to $10^{-3}$.">
+        <tr id="Analyzing long-term behaviors in high-dimensional nonlinear dynamical systems remains a significant challenge. The Koopman operator framework has emerged as a powerful tool to address this issue by providing a globally linear perspective on nonlinear dynamics. However, existing methods for approximating the Koopman operator and its spectral components, particularly in large-scale systems, often lack robust theoretical guarantees. Residual Dynamic Mode Decomposition (ResDMD) introduces a spectral residual measure to assess the convergence of the estimated Koopman spectrum, which helps filter out spurious spectral components. Nevertheless, it depends on pre-computed spectra, thereby inheriting their inaccuracies. To overcome its limitations, we introduce the Neural Network-ResDMD (NN-ResDMD), a method that directly estimates Koopman spectral components by minimizing the spectral residual. By leveraging neural networks, NN-ResDMD automatically identifies the optimal basis functions of the Koopman invariant subspace, eliminating the need for manual selection and improving the reliability of the analysis. Experiments on physical and biological systems demonstrate that NN-ResDMD significantly improves both accuracy and scalability, making it an effective tool for analyzing complex dynamical systems.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/1813775ba7037766128f7424de2d1af0d4c0a917" target='_blank'>
-              Data-driven optimal control of unknown nonlinear dynamical systems using the Koopman operator
+          <td><a href="https://www.semanticscholar.org/paper/2438e0ff050ca024f82d1b4b41c315634b0150b8" target='_blank'>
+              NN-ResDMD: Learning Koopman Representations for Complex Dynamics with Spectral Residuals
               </a>
             </td>
           <td>
-            Zhexuan Zeng, Rui Zhou, Yiming Meng, Jun Liu
+            Yuanchao Xu, Kaidi Shao, Nikos Logothetis, Zhongwei Shen
           </td>
-          <td>2024-12-02</td>
+          <td>2025-01-01</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>9</td>
+          <td>0</td>
         </tr>
 
-        <tr id="Solving partial differential equations (PDEs) is essential in scientific forecasting and fluid dynamics. Traditional approaches often incur expensive computational costs and trade-offs in efficiency and accuracy. Recent deep neural networks improve accuracy but require quality training data. Physics-informed neural networks (PINNs) effectively integrate physical laws, reducing data reliance in limited sample scenarios. A novel machine-learning framework, Chebyshev physics-informed Kolmogorov-Arnold network (ChebPIKAN), is proposed to integrate the robust architectures of Kolmogorov-Arnold networks (KAN) with physical constraints to enhance calculation accuracy of PDEs for fluid mechanics. We explore the fundamentals of KAN, emphasis on the advantages of using the orthogonality of Chebyshev polynomial basis functions in spline fitting, and describe the incorporation of physics-informed loss functions tailored to specific PDEs in fluid dynamics, including Allen-Cahn equation, nonlinear Burgers equation, two-dimensional Helmholtz equations, two-dimensional Kovasznay flow and two-dimensional Navier-Stokes equations. Extensive experiments demonstrate that the proposed ChebPIKAN model significantly outperforms standard KAN architecture in solving various PDEs by embedding essential physical information more effectively. These results indicate that augmenting KAN with physical constraints can not only alleviate overfitting issues of KAN but also improve extrapolation performance. Consequently, this study highlights the potential of ChebPIKAN as a powerful tool in computational fluid dynamics, proposing a path toward fast and reliable predictions in fluid mechanics and beyond.">
+        <tr id="In complex physical systems, conventional differential equations often fall short in capturing non-local and memory effects, as they are limited to local dynamics and integer-order interactions. This study introduces a stepwise data-driven framework for discovering fractional differential equations (FDEs) directly from data. FDEs, known for their capacity to model non-local dynamics with fewer parameters than integer-order derivatives, can represent complex systems with long-range interactions. Our framework applies deep neural networks as surrogate models for denoising and reconstructing sparse and noisy observations while using Gaussian-Jacobi quadrature to handle the challenges posed by singularities in fractional derivatives. To optimize both the sparse coefficients and fractional order, we employ an alternating optimization approach that combines sparse regression with global optimization techniques. We validate the framework across various datasets, including synthetic anomalous diffusion data, experimental data on the creep behavior of frozen soils, and single-particle trajectories modeled by L\'{e}vy motion. Results demonstrate the framework's robustness in identifying the structure of FDEs across diverse noise levels and its capacity to capture integer-order dynamics, offering a flexible approach for modeling memory effects in complex systems.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/4dd0f46fe2d56b8d6854361349a8968b87261e10" target='_blank'>
-              Physics-informed Kolmogorov-Arnold Network with Chebyshev Polynomials for Fluid Mechanics
+          <td><a href="https://www.semanticscholar.org/paper/ea19e187b5ce3208f332cc671f31694cb533a2f6" target='_blank'>
+              A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems
               </a>
             </td>
           <td>
-            Chunyu Guo, Lucheng Sun, Shilong Li, Zelong Yuan, Chao Wang
+            Xiangnan Yu, Hao Xu, Zhiping Mao, Hongguang Sun, Yong Zhang, Dong-juan Zhang, Yuntian Chen
           </td>
-          <td>2024-11-07</td>
+          <td>2024-12-05</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>2</td>
+          <td>11</td>
         </tr>
 
-        <tr id="We present a data-driven framework for learning hydrodynamic equations from particle-based simulations of active matter. Our method leverages coarse-graining in both space and time to bridge microscopic particle dynamics with macroscopic continuum models. By employing spectral representations and sparse regression, we efficiently estimate partial differential equations (PDEs) that capture collective behaviors such as flocking and phase separation. This approach, validated using hydrodynamic descriptions of the Vicsek model and Active Brownian particles, demonstrates the potential of data-driven strategies to uncover the universal features of collective dynamics in active matter systems.">
+        <tr id="Nonlinear optimal control is vital for numerous applications but remains challenging for unknown systems due to the difficulties in accurately modelling dynamics and handling computational demands, particularly in high-dimensional settings. This work develops a theoretically certifiable framework that integrates a modified Koopman operator approach with model-based reinforcement learning to address these challenges. By relaxing the requirements on observable functions, our method incorporates nonlinear terms involving both states and control inputs, significantly enhancing system identification accuracy. Moreover, by leveraging the power of neural networks to solve partial differential equations (PDEs), our approach is able to achieving stabilizing control for high-dimensional dynamical systems, up to 9-dimensional. The learned value function and control laws are proven to converge to those of the true system at each iteration. Additionally, the accumulated cost of the learned control closely approximates that of the true system, with errors ranging from $10^{-5}$ to $10^{-3}$.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/f810d004143ec489a081b2450ad6c57b3f181f6c" target='_blank'>
-              Estimation of spatial and time scales of collective behaviors of active matters through learning hydrodynamic equations from particle dynamics
+          <td><a href="https://www.semanticscholar.org/paper/1813775ba7037766128f7424de2d1af0d4c0a917" target='_blank'>
+              Data-driven optimal control of unknown nonlinear dynamical systems using the Koopman operator
               </a>
             </td>
           <td>
-            Bappaditya Roy, N. Yoshinaga
+            Zhexuan Zeng, Rui Zhou, Yiming Meng, Jun Liu
           </td>
-          <td>2024-11-06</td>
+          <td>2024-12-02</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>18</td>
+          <td>9</td>
         </tr>
 
         <tr id="Conventional notions of generalization often fail to describe the ability of learned models to capture meaningful information from dynamical data. A neural network that learns complex dynamics with a small test error may still fail to reproduce its \emph{physical} behavior, including associated statistical moments and Lyapunov exponents. To address this gap, we propose an ergodic theoretic approach to generalization of complex dynamical models learned from time series data. Our main contribution is to define and analyze generalization of a broad suite of neural representations of classes of ergodic systems, including chaotic systems, in a way that captures emulating underlying invariant, physical measures. Our results provide theoretical justification for why regression methods for generators of dynamical systems (Neural ODEs) fail to generalize, and why their statistical accuracy improves upon adding Jacobian information during training. We verify our results on a number of ergodic chaotic systems and neural network parameterizations, including MLPs, ResNets, Fourier Neural layers, and RNNs.">
@@ -1116,7 +1071,7 @@ <h3 id="recommended_articles">Recommended articles on <i>Symbolic regression</i>
           </td>
           <td>2024-11-09</td>
           <td>ArXiv</td>
-          <td>0</td>
+          <td>1</td>
           <td>8</td>
         </tr>
 
@@ -1195,19 +1150,19 @@ <h3 id="recommended_articles">Recommended articles on <i>Symbolic regression</i>
           <td>0</td>
         </tr>
 
-        <tr id="Dynamic mode decomposition (DMD) is a popular approach to analyzing and modeling fluid flows. In practice, datasets are almost always corrupted to some degree by noise. The vanilla DMD is highly noise-sensitive, which is why many algorithmic extensions for improved robustness exist. We introduce a flexible optimization approach that merges available ideas for improved accuracy and robustness. The approach simultaneously identifies coherent dynamics and noise in the data. In tests on the laminar flow past a cylinder, the method displays strong noise robustness and high levels of accuracy.">
+        <tr id="In the context of hybrid twins, a data-driven enrichment is added to the physics-based solution to represent with higher accuracy the reference solution assumed to be known at different points in the physical domain. Such an approach enables better predictions. However, the data-driven enrichment is usually represented by a regression, whose main drawbacks are (i) the difficulty of understanding the subjacent physics and (ii) the risks induced by the data-driven model extrapolation. This paper proposes a procedure enabling the extraction of a differential operator associated with the enrichment provided by the data-driven regression. For that purpose, a sparse Singular Value Decomposition, SVD, is introduced. It is then employed, first, in a full operator representation regularized optimization problem, where sparsity is promoted, leading to a linear programming problem, and then in a tensor decomposition of the operator’s identification procedure. The results show the ability of the method to identify the exact missing operators from the model. The regularized optimization problem was also able to identify the weights of the missing terms with a relative error of about 10% on average, depending on the selected use case.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/a312a5639e3733accf76f30959ded02c524e8b80" target='_blank'>
-              An optimized dynamic mode decomposition to identify coherent dynamics in noisy flow data
+          <td><a href="https://www.semanticscholar.org/paper/7bf2105b078261e20b475bc82ccb46d0caa4ad79" target='_blank'>
+              Discovering PDEs Corrections from Data Within a Hybrid Modeling Framework
               </a>
             </td>
           <td>
-            Andre Weiner, Janis Geise
+            C. Ghnatios, F. Chinesta
           </td>
-          <td>2024-11-07</td>
-          <td>ArXiv</td>
+          <td>2024-12-24</td>
+          <td>Mathematics</td>
           <td>0</td>
-          <td>1</td>
+          <td>14</td>
         </tr>
 
         <tr id="The identification of dynamical systems from data is essential in control theory, enabling the creation of mathematical models that accurately represent the behavior of complex systems. However, real-world applications often present challenges such as the unknown dimensionality of the system and limited access to measurements, particularly in partially observed systems. The Hankel alternative view of Koopman (HAVOK) method offers a data-driven approach to identify linear representations of nonlinear systems, but it often overlooks the influence of external control signals (inputs) and disturbances. This paper introduces a novel input-aware modeling method for unstable linear systems using data-driven Koopman analysis. By explicitly incorporating the impact of inputs and disturbances, our method enhances the accuracy and robustness of system identification, even in the face of incomplete observations. The proposed approach leverages Koopman operator theory on augmented state-input data to capture both the intrinsic dynamics and the system’s sensitivity to external control. Through extensive numerical examples, we demonstrate the effectiveness of our method in accurately identifying and predicting the behavior of various dynamical systems, including real-world nonlinear systems and simulated unstable linear systems with and without disturbances. The results highlight the potential of our approach to advance the field of system identification and control, offering a powerful tool for modeling and analyzing complex systems in diverse applications.">
@@ -1240,34 +1195,19 @@ <h3 id="recommended_articles">Recommended articles on <i>Symbolic regression</i>
           <td>17</td>
         </tr>
 
-        <tr id="Physics-informed neural networks (PINNs) have made significant strides in modeling dynamical systems governed by partial differential equations (PDEs). However, their generalization capabilities across varying scenarios remain limited. To overcome this limitation, we propose PIDO, a novel physics-informed neural PDE solver designed to generalize effectively across diverse PDE configurations, including varying initial conditions, PDE coefficients, and training time horizons. PIDO exploits the shared underlying structure of dynamical systems with different properties by projecting PDE solutions into a latent space using auto-decoding. It then learns the dynamics of these latent representations, conditioned on the PDE coefficients. Despite its promise, integrating latent dynamics models within a physics-informed framework poses challenges due to the optimization difficulties associated with physics-informed losses. To address these challenges, we introduce a novel approach that diagnoses and mitigates these issues within the latent space. This strategy employs straightforward yet effective regularization techniques, enhancing both the temporal extrapolation performance and the training stability of PIDO. We validate PIDO on a range of benchmarks, including 1D combined equations and 2D Navier-Stokes equations. Additionally, we demonstrate the transferability of its learned representations to downstream applications such as long-term integration and inverse problems.">
+        <tr id="Differentiable Programming for scientific machine learning (SciML) has recently seen considerable interest and success, as it directly embeds neural networks inside PDEs, often called as NeuralPDEs, derived from first principle physics. Therefore, there is a widespread assumption in the community that NeuralPDEs are more trustworthy and generalizable than black box models. However, like any SciML model, differentiable programming relies predominantly on high-quality PDE simulations as"ground truth"for training. However, mathematics dictates that these are only discrete numerical approximations of the true physics. Therefore, we ask: Are NeuralPDEs and differentiable programming models trained on PDE simulations as physically interpretable as we think? In this work, we rigorously attempt to answer these questions, using established ideas from numerical analysis, experiments, and analysis of model Jacobians. Our study shows that NeuralPDEs learn the artifacts in the simulation training data arising from the discretized Taylor Series truncation error of the spatial derivatives. Additionally, NeuralPDE models are systematically biased, and their generalization capability is likely enabled by a fortuitous interplay of numerical dissipation and truncation error in the training dataset and NeuralPDE, which seldom happens in practical applications. This bias manifests aggressively even in relatively accessible 1-D equations, raising concerns about the veracity of differentiable programming on complex, high-dimensional, real-world PDEs, and in dataset integrity of foundation models. Further, we observe that the initial condition constrains the truncation error in initial-value problems in PDEs, thereby exerting limitations to extrapolation. Finally, we demonstrate that an eigenanalysis of model weights can indicate a priori if the model will be inaccurate for out-of-distribution testing.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/85bddf6fb22acf4165ea5d68f285e2eb0f363ada" target='_blank'>
-              Advancing Generalization in PINNs through Latent-Space Representations
+          <td><a href="https://www.semanticscholar.org/paper/cdb9b53b1f243b0a088c1b9e5a30f657cb339642" target='_blank'>
+              What You See is Not What You Get: Neural Partial Differential Equations and The Illusion of Learning
               </a>
             </td>
           <td>
-            Honghui Wang, Yifan Pu, Shiji Song, Gao Huang
+            Arvind Mohan, A. Chattopadhyay, Jonah Miller
           </td>
-          <td>2024-11-28</td>
+          <td>2024-11-22</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>11</td>
-        </tr>
-
-        <tr id="Surrogate modeling of non-linear oscillator networks remains challenging due to discrepancies between simplified analytical models and real-world complexity. To bridge this gap, we investigate hybrid reservoir computing, combining reservoir computing with"expert"analytical models. Simulating the absence of an exact model, we first test the surrogate models with parameter errors in their expert model. Second, we assess their performance when their expert model lacks key non-linear coupling terms present in an extended ground-truth model. We focus on short-term forecasting across diverse dynamical regimes, evaluating the use of these surrogates for control applications. We show that hybrid reservoir computers generally outperform standard reservoir computers and exhibit greater robustness to parameter tuning. Notably, unlike standard reservoir computers, the performance of the hybrid does not degrade when crossing an observed spectral radius threshold. Furthermore, there is good performance for dynamical regimes not accessible to the expert model, demonstrating the contribution of the reservoir.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/386eb3a2659f46dd6c23f416cd80b5f5633216d6" target='_blank'>
-              Modeling Nonlinear Oscillator Networks Using Physics-Informed Hybrid Reservoir Computing
-              </a>
-            </td>
-          <td>
-            Andrew Shannon, Conor Houghton, David Barton, Martin Homer
-          </td>
-          <td>2024-11-07</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>0</td>
+          <td>16</td>
         </tr>
 
         <tr id="None">
@@ -1285,230 +1225,300 @@ <h3 id="recommended_articles">Recommended articles on <i>Symbolic regression</i>
           <td>9</td>
         </tr>
 
-        <tr id="Externally driven dense packings of particles can exhibit nonlinear wave phenomena that are not described by effective medium theory or linearized approximate models. Such nontrivial wave responses can be exploited to design sound-focusing/scrambling devices, acoustic filters, and analog computational units. At high amplitude vibrations or low confinement pressures, the effect of nonlinear particle contacts becomes increasingly noticeable, and the interplay of nonlinearity, disorder, and discreteness in the system gives rise to remarkable properties, particularly useful in designing structures with exotic properties. In this paper, we build upon the data-driven methods in dynamical system analysis and show that the Koopman spectral theory can be applied to granular crystals, enabling their phase space analysis beyond the linearizable regime and without recourse to any approximations considered in the previous works. We show that a deep neural network can map the dynamics to a latent space where the essential nonlinearity of the granular system unfolds into a high-dimensional linear space. As a proof of concept, we use data from numerical simulations of a two-particle system and evaluate the accuracy of the trajectory predictions under various initial conditions. By incorporating data from experimental measurements, our proposed framework can directly capture the underlying dynamics without imposing any assumptions about the physics model. Spectral analysis of the trained surrogate system can help bridge the gap between the simulation results and the physical realization of granular crystals and facilitate the inverse design of materials with desired behaviors.">
+        <tr id="Differential equations offer a foundational yet powerful framework for modeling interactions within complex dynamic systems and are widely applied across numerous scientific fields. One common challenge in this area is estimating the unknown parameters of these dynamic relationships. However, traditional numerical optimization methods rely on the selection of initial parameter values, making them prone to local optima. Meanwhile, deep learning and Bayesian methods require training models on specific differential equations, resulting in poor versatility. This paper reformulates the parameter estimation problem of differential equations as an optimization problem by introducing the concept of particles from the particle swarm optimization algorithm. Building on reinforcement learning-based particle swarm optimization (RLLPSO), this paper proposes a novel method, DERLPSO, for estimating unknown parameters of differential equations. We compared its performance on three typical ordinary differential equations with the state-of-the-art methods, including the RLLPSO algorithm, traditional numerical methods, deep learning approaches, and Bayesian methods. The experimental results demonstrate that our DERLPSO consistently outperforms other methods in terms of performance, achieving an average Mean Square Error of 1.13e-05, which reduces the error by approximately 4 orders of magnitude compared to other methods. Apart from ordinary differential equations, our DERLPSO also show great promise for estimating unknown parameters of partial differential equations. The DERLPSO method proposed in this paper has high accuracy, is independent of initial parameter values, and possesses strong versatility and stability. This work provides new insights into unknown parameter estimation for differential equations.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/c6b8cf343696909c747e3feaeec4995eb6b9c375" target='_blank'>
-              Data-driven Modeling of Granular Chains with Modern Koopman Theory
+          <td><a href="https://www.semanticscholar.org/paper/42606e840f07d335407f696a30f618399ba44ee4" target='_blank'>
+              Estimating unknown parameters in differential equations with a reinforcement learning based PSO method
               </a>
             </td>
           <td>
-            Atoosa Parsa, James P. Bagrow, Corey S. O'Hern, Rebecca Kramer‐Bottiglio, Josh C. Bongard
+            Wenkui Sun, Xiaoya Fan, Lijuan Jia, Tinyi Chu, S. Yau, Rongling Wu, Zhong Wang
           </td>
-          <td>2024-11-01</td>
+          <td>2024-11-13</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>26</td>
+          <td>112</td>
         </tr>
 
-        <tr id="Continuous monitoring and real-time control of high-dimensional distributed systems are often crucial in applications to ensure a desired physical behavior, without degrading stability and system performances. Traditional feedback control design that relies on full-order models, such as high-dimensional state-space representations or partial differential equations, fails to meet these requirements due to the delay in the control computation, which requires multiple expensive simulations of the physical system. The computational bottleneck is even more severe when considering parametrized systems, as new strategies have to be determined for every new scenario. To address these challenges, we propose a real-time closed-loop control strategy enhanced by nonlinear non-intrusive Deep Learning-based Reduced Order Models (DL-ROMs). Specifically, in the offline phase, (i) full-order state-control pairs are generated for different scenarios through the adjoint method, (ii) the essential features relevant for control design are extracted from the snapshots through a combination of Proper Orthogonal Decomposition (POD) and deep autoencoders, and (iii) the low-dimensional policy bridging latent control and state spaces is approximated with a feedforward neural network. After data generation and neural networks training, the optimal control actions are retrieved in real-time for any observed state and scenario. In addition, the dynamics may be approximated through a cheap surrogate model in order to close the loop at the latent level, thus continuously controlling the system in real-time even when full-order state measurements are missing. The effectiveness of the proposed method, in terms of computational speed, accuracy, and robustness against noisy data, is finally assessed on two different high-dimensional optimal transport problems, one of which also involving an underlying fluid flow.">
+        <tr id="Prediction of Kelvin-Helmholtz instability (KHI) is crucial across various fields, requiring extensive high-fidelity data. However, experimental data are often sparse and noisy, while simulated data may lack credibility due to discrepancies with real-world configurations and parameters. This underscores the need for field reconstruction and parameter inference from sparse, noisy data, which constitutes inverse problems. Based on the physics-informed neural networks (PINNs), the KH-PINN framework is established in this work to solve the inverse problems of KHI flows. By incorporating the governing physical equations, KH-PINN reconstructs continuous flow fields and infer unknown transport parameters from sparse, noisy observed data. The 2D unsteady incompressible flows with both constant and variable densities are studied. To our knowledge, this is the first application of PINNs to unsteady incompressible flows with variable densities. To address the spatiotemporal multiscale issue and enhance the reconstruction accuracy of small-scale structures, the multiscale embedding (ME) strategy is adopted. To address the magnitude multiscale issue and enhance the reconstruction accuracy of small-magnitude velocities, which are critical for KHI problems, the small-velocity amplification (SVA) strategy is proposed. The results demonstrate that KH-PINN can accurately reconstruct the fields with complex, evolving vortices and infer unknown parameters across a broad range of Reynolds numbers. Additionally, the energy-decaying and entropy-increasing curves are accurately obtained. The effectiveness of ME and SVA is validated through comparative studies, and the anti-noise and few-shot learning capabilities of KH-PINN are also validated. The code for this work is available at https://github.com/CAME-THU/KH-PINN.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/ca78121ffa14df2e312fd8c2aa951f545094f942" target='_blank'>
-              Latent feedback control of distributed systems in multiple scenarios through deep learning-based reduced order models
+          <td><a href="https://www.semanticscholar.org/paper/ef49b25ebb936ec968b8484afa447714276f1d66" target='_blank'>
+              KH-PINN: Physics-informed neural networks for Kelvin-Helmholtz instability with spatiotemporal and magnitude multiscale
               </a>
             </td>
           <td>
-            Matteo Tomasetto, Francesco Braghin, Andrea Manzoni
+            Jiahao Wu, Yuxin Wu, Xin Li, Guihua Zhang
           </td>
-          <td>2024-12-13</td>
+          <td>2024-11-12</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>1</td>
+          <td>2</td>
         </tr>
 
-        <tr id="We propose an entropy-stable conservative flux form neural network (CFN) that integrates classical numerical conservation laws into a data-driven framework using the entropy-stable, second-order, and non-oscillatory Kurganov-Tadmor (KT) scheme. The proposed entropy-stable CFN uses slope limiting as a denoising mechanism, ensuring accurate predictions in both noisy and sparse observation environments, as well as in both smooth and discontinuous regions. Numerical experiments demonstrate that the entropy-stable CFN achieves both stability and conservation while maintaining accuracy over extended time domains. Furthermore, it successfully predicts shock propagation speeds in long-term simulations, {\it without} oracle knowledge of later-time profiles in the training data.">
+        <tr id="In this study, we apply two pillars of Scientific Machine Learning: Neural Ordinary Differential Equations (Neural ODEs) and Universal Differential Equations (UDEs) to the Lotka Volterra Predator Prey Model, a fundamental ecological model describing the dynamic interactions between predator and prey populations. The Lotka-Volterra model is critical for understanding ecological dynamics, population control, and species interactions, as it is represented by a system of differential equations. In this work, we aim to uncover the underlying differential equations without prior knowledge of the system, relying solely on training data and neural networks. Using robust modeling in the Julia programming language, we demonstrate that both Neural ODEs and UDEs can be effectively utilized for prediction and forecasting of the Lotka-Volterra system. More importantly, we introduce the forecasting breakdown point: the time at which forecasting fails for both Neural ODEs and UDEs. We observe how UDEs outperform Neural ODEs by effectively recovering the underlying dynamics and achieving accurate forecasting with significantly less training data. Additionally, we introduce Gaussian noise of varying magnitudes (from mild to high) to simulate real-world data perturbations and show that UDEs exhibit superior robustness, effectively recovering the underlying dynamics even in the presence of noisy data, while Neural ODEs struggle with high levels of noise. Through extensive hyperparameter optimization, we offer insights into neural network architectures, activation functions, and optimizers that yield the best results. This study opens the door to applying Scientific Machine Learning frameworks for forecasting tasks across a wide range of ecological and scientific domains.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/d02e1e903961d819a3723754d4e2bca0440d9e25" target='_blank'>
-              Entropy stable conservative flux form neural networks
+          <td><a href="https://www.semanticscholar.org/paper/851b83ce92820fa6d217f0d4cb4108121c1dd6d2" target='_blank'>
+              Scientific machine learning in ecological systems: A study on the predator-prey dynamics
               </a>
             </td>
           <td>
-            Lizuo Liu, Tongtong Li, Anne Gelb, Yoonsang Lee
+            Ranabir Devgupta, R. Dandekar, R. Dandekar, S. Panat
           </td>
-          <td>2024-11-04</td>
+          <td>2024-11-11</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>1</td>
+          <td>3</td>
         </tr>
 
-        <tr id="This work introduces methods for validating neu-ral network solutions in the context of governing equations and Hamiltonian structures, crucial for accurately representing physical systems. The first approach focuses on the structural preservation of the Hamiltonian system, emphasizing the re-lationship between coordinates and momentum in the state-space representation. The second method utilizes Monte Carlo techniques, generating distributions of parameters and external, dissipative forces to validate the neural network model. This provides a robust framework for assessing the neural network's compliance with the governing equations of the physical system it aims to model. A case study involving a simple pendulum is presented to test the proposed validation techniques. The results highlight the importance of aligning the neural network training approach with the relevant validation criteria for the application, as different methods exhibit varying performance in terms of mean squared error, Hamiltonian structure preservation, and derivative-based verification. This nuanced approach underscores the necessity of tailoring neural network training strategies to enhance the reliability of predictions in modeling complex dynamical systems.">
+        <tr id="The Physics-Informed Neural Network (PINN) is an innovative approach to solve a diverse array of partial differential equations (PDEs) leveraging the power of neural networks. This is achieved by minimizing the residual loss associated with the explicit physical information, usually coupled with data derived from initial and boundary conditions. However, a challenge arises in the context of nonlinear conservation laws where derivatives are undefined at shocks, leading to solutions that deviate from the true physical phenomena. To solve this issue, the physical solution must be extracted from the weak formulation of the PDE and is typically further bounded by entropy conditions. Within the numerical framework, finite volume methods (FVM) are employed to address conservation laws. These methods resolve the integral form of conservation laws and delineate the shock characteristics. Inspired by the principles underlying FVM, this paper introduces a novel Coupled Integrated PINN methodology that involves fitting the integral solutions of equations using additional neural networks. This technique not only augments the conventional PINN's capability in modeling shock waves, but also eliminates the need for spatial and temporal discretization. As such, it bypasses the complexities of numerical integration and reconstruction associated with non-convex fluxes. Finally, we show that the proposed new Integrated PINN performs well in conservative law and outperforms the vanilla PINN when tackle the challenging shock problems using examples of Burger's equation, Buckley-Leverett Equation and Euler System.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/a25417a5c5b9e64b6e185b8da2a982fa36f83a55" target='_blank'>
-              Comparison of Neural Network Training Approaches That Preserve Physical Properties of Cyber-Physical System
+          <td><a href="https://www.semanticscholar.org/paper/0420e731a61400300a3eb3bbbe9a957957e1adfa" target='_blank'>
+              Coupled Integral PINN for conservation law
               </a>
             </td>
           <td>
-            Josafat Leal Filho, Stephan Paul, Antônio Augusto Fröhlich
+            Yeping Wang, Shihao Yang
           </td>
-          <td>2024-11-26</td>
-          <td>2024 XIV Brazilian Symposium on Computing Systems Engineering (SBESC)</td>
+          <td>2024-11-18</td>
+          <td>ArXiv</td>
           <td>0</td>
           <td>0</td>
         </tr>
 
-        <tr id="This article develops a novel data assimilation methodology, addressing challenges that are common in real-world settings, such as severe sparsity of observations, lack of reliable models, and non-stationarity of the system dynamics. These challenges often cause identifiability issues and can confound model parameter initialization, both of which can lead to estimated models with unrealistic qualitative dynamics and induce deeper parameter estimation errors. The proposed methodology's objective function is constructed as a sum of components, each serving a different purpose: enforcing point-wise and distribution-wise agreement between data and model output, enforcing agreement of variables and parameters with a model provided, and penalizing unrealistic rapid parameter changes, unless they are due to external drivers or interventions. This methodology was motivated by, developed and evaluated in the context of estimating blood glucose levels in different medical settings. Both simulated and real data are used to evaluate the methodology from different perspectives, such as its ability to estimate unmeasured variables, its ability to reproduce the correct qualitative blood glucose dynamics, how it manages known non-stationarity, and how it performs when given a range of dense and severely sparse data. The results show that a multicomponent cost function can balance the minimization of point-wise errors with global properties, robustly preserving correct qualitative dynamics and managing data sparsity.">
+        <tr id="In this paper, we present a new parametrization to perform direct data-driven analysis and controller synthesis for the error-in-variables case. To achieve this, we employ the Sherman-Morrison-Woodbury formula to transform the problem into a linear fractional transformation (LFT) with unknown measurement errors and disturbances as uncertainties. For bounded uncertainties, we apply robust control techniques to derive a guaranteed upper bound on the H2-norm of the unknown true system. To this end, a single semidefinite program (SDP) needs to be solved, with complexity that is independent of the amount of data. Furthermore, we exploit the signal-to-noise ratio to provide a data-dependent condition, that characterizes whether the proposed parametrization can be employed. The modular formulation allows to extend this framework to controller synthesis with different performance criteria, input-output settings, and various system properties. Finally, we validate the proposed approach through a numerical example.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/118954ef64b3260d452a342f5b83a0eab540303f" target='_blank'>
-              A new approach to data assimilation initialization problems with sparse data using multiple cost functions
+          <td><a href="https://www.semanticscholar.org/paper/de5b2106c1748e3318c926b97181ff89d1cf864c" target='_blank'>
+              A System Parametrization for Direct Data-Driven Analysis and Control with Error-in-Variables
               </a>
             </td>
           <td>
-            David J. Abers, G. Hripcsak, Lena Mamykina, Melike Sirlanci, E. Tabak
+            Felix Brändle, Frank Allgöwer
           </td>
-          <td>2024-11-04</td>
+          <td>2024-11-11</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>31</td>
+          <td>4</td>
         </tr>
 
-        <tr id="Differential equations offer a foundational yet powerful framework for modeling interactions within complex dynamic systems and are widely applied across numerous scientific fields. One common challenge in this area is estimating the unknown parameters of these dynamic relationships. However, traditional numerical optimization methods rely on the selection of initial parameter values, making them prone to local optima. Meanwhile, deep learning and Bayesian methods require training models on specific differential equations, resulting in poor versatility. This paper reformulates the parameter estimation problem of differential equations as an optimization problem by introducing the concept of particles from the particle swarm optimization algorithm. Building on reinforcement learning-based particle swarm optimization (RLLPSO), this paper proposes a novel method, DERLPSO, for estimating unknown parameters of differential equations. We compared its performance on three typical ordinary differential equations with the state-of-the-art methods, including the RLLPSO algorithm, traditional numerical methods, deep learning approaches, and Bayesian methods. The experimental results demonstrate that our DERLPSO consistently outperforms other methods in terms of performance, achieving an average Mean Square Error of 1.13e-05, which reduces the error by approximately 4 orders of magnitude compared to other methods. Apart from ordinary differential equations, our DERLPSO also show great promise for estimating unknown parameters of partial differential equations. The DERLPSO method proposed in this paper has high accuracy, is independent of initial parameter values, and possesses strong versatility and stability. This work provides new insights into unknown parameter estimation for differential equations.">
+        <tr id="We develop compositional learning algorithms for coupled dynamical systems. While deep learning has proven effective at modeling complex relationships from data, compositional couplings between system components typically introduce algebraic constraints on state variables, posing challenges to many existing data-driven approaches to modeling dynamical systems. Towards developing deep learning models for constrained dynamical systems, we introduce neural port-Hamiltonian differential algebraic equations (N-PHDAEs), which use neural networks to parametrize unknown terms in both the differential and algebraic components of a port-Hamiltonian DAE. To train these models, we propose an algorithm that uses automatic differentiation to perform index reduction, automatically transforming the neural DAE into an equivalent system of neural ordinary differential equations (N-ODEs), for which established model inference and backpropagation methods exist. The proposed compositional modeling framework and learning algorithms may be applied broadly to learn control-oriented models of dynamical systems in a variety of application areas, however, in this work, we focus on their application to the modeling of electrical networks. Experiments simulating the dynamics of nonlinear circuits exemplify the benefits of our approach: the proposed N-PHDAE model achieves an order of magnitude improvement in prediction accuracy and constraint satisfaction when compared to a baseline N-ODE over long prediction time horizons. We also validate the compositional capabilities of our approach through experiments on a simulated D.C. microgrid: we train individual N-PHDAE models for separate grid components, before coupling them to accurately predict the behavior of larger-scale networks.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/42606e840f07d335407f696a30f618399ba44ee4" target='_blank'>
-              Estimating unknown parameters in differential equations with a reinforcement learning based PSO method
+          <td><a href="https://www.semanticscholar.org/paper/2388b39794f5824c68a3b768d02938b68a1c228a" target='_blank'>
+              Neural Port-Hamiltonian Differential Algebraic Equations for Compositional Learning of Electrical Networks
               </a>
             </td>
           <td>
-            Wenkui Sun, Xiaoya Fan, Lijuan Jia, Tinyi Chu, S. Yau, Rongling Wu, Zhong Wang
+            Cyrus Neary, Nathan Tsao, U. Topcu
           </td>
-          <td>2024-11-13</td>
+          <td>2024-12-15</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>112</td>
+          <td>49</td>
         </tr>
 
-        <tr id="A semigroup characterization, or equivalently, a characterization by the generator, is a classical technique used to describe continuous-time nonlinear dynamical systems. In the realm of data-driven learning for an unknown nonlinear system, one must estimate the generator of the semigroup of the system's transfer operators (also known as the semigroup of Koopman operators) based on discrete-time observations and verify convergence to the true generator in an appropriate sense. As the generator encodes essential transient transitional information of the system, challenges arise for some existing methods that rely on accurately estimating the time derivatives of the state with constraints on the observation rate. Recent literature develops a technique that avoids the use of time derivatives by employing the logarithm of a Koopman operator. However, the validity of this method has been demonstrated only within a restrictive function space and requires knowledge of the operator's spectral properties. In this paper, we propose a resolvent-type method for learning the system generator to relax the requirements on the observation frequency and overcome the constraints of taking operator logarithms. We also provide numerical examples to demonstrate its effectiveness in applications of system identification and constructing Lyapunov functions.">
+        <tr id="
+ Characterizing the nonlinear behavior of dynamical systems near the stability boundary is a critical step toward understanding, designing, and controlling systems prone to stability concerns. Traditional methods for bifurcation analysis in both experimental systems and large-dimensional models are often hindered either by the absence of an accurate model or by the analytical complexity involved. This paper presents a novel approach that combines the theoretical frameworks of nonlinear reduced-order modeling and stability analysis in dynamical systems with advanced machine learning techniques to perform bifurcation analysis in dynamical systems. By focusing on a low-dimensional nonlinear invariant manifold, this work proposes a data-driven methodology that simplifies the process of bifurcation analysis in dynamical systems. The core of our approach lies in utilizing carefully designed neural networks to identify nonlinear transformations that map observation space into reduced manifold coordinates in its normal form where bifurcation analysis can be performed. The unique integration of analytical and data-driven approaches in the proposed method enables the learning of these transformations and the performance of bifurcation analysis with a limited number of trajectories. Therefore, this approach improves bifurcation analysis in model-less experimental systems and cost-sensitive high-fidelity simulations. The effectiveness of this approach is demonstrated across several examples.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/8a7eb6fad44eaddd9475549bc4d894991dfcd620" target='_blank'>
-              Resolvent-Type Data-Driven Learning of Generators for Unknown Continuous-Time Dynamical Systems
+          <td><a href="https://www.semanticscholar.org/paper/3390fedb1047db4aa3bba8bfb0c549ae79e43689" target='_blank'>
+              Bifurcation analysis in dynamical systems through integration of machine learning and dynamical systems theory
               </a>
             </td>
           <td>
-            Yiming Meng, Rui Zhou, Melkior Ornik, Jun Liu
+            Nami Mogharabin, Amin Ghadami
           </td>
-          <td>2024-11-01</td>
-          <td>ArXiv</td>
-          <td>1</td>
-          <td>10</td>
+          <td>2024-11-27</td>
+          <td>Journal of Computational and Nonlinear Dynamics</td>
+          <td>0</td>
+          <td>2</td>
         </tr>
 
-        <tr id="This paper introduces an online approach for identifying time-varying subspaces defined by linear dynamical systems, leveraging optimization on the Grassmannian manifold leading to the Grassmannian Recursive Algorithm for Tracking (GREAT) method. The approach of representing linear systems by non-parametric subspace models has received significant interest in the field of data-driven control recently. We view subspaces as points on the Grassmannian manifold, and therefore, tracking is achieved by performing optimization on the manifold. At each time step, a single measurement from the current subspace corrupted by a bounded error is available. The subspace estimate is updated online using Grassmannian gradient descent on a cost function incorporating a window of the most recent data. Under suitable assumptions on the signal-to-noise ratio of the online data and the subspace's rate of change, we establish theoretical guarantees for the resulting algorithm. More specifically, we prove an exponential convergence rate and provide a consistent uncertainty quantification of the estimates in terms of an upper bound on their distance to the true subspace. The applicability of the proposed algorithm is demonstrated by means of numerical examples, and it is shown to compare favorably with competing parametric system identification methods.">
+        <tr id="
+ This paper introduces a new neural network architecture designed to forecast high-dimensional spatio-temporal data using only sparse measurements. The architecture utilizes a two-stage end-to-end framework that combines neural ordinary differential equation (NODE) models with vision transformers (ViTs). Initially, our approach models the underlying dynamics of complex systems within a low-dimensional space and then reconstructs the corresponding high-dimensional spatial fields. Traditional methods often involve decoding high-dimensional spatial fields before modeling the dynamics, while others use an encoder to transition from high-dimensional observations to a latent space for dynamic modeling. In contrast, our approach directly uses sparse measurements to model the dynamics, bypassing the need for an encoder. This direct approach simplifies the modeling process, reduces computational complexity, and enhances the efficiency and scalability of the method for large datasets. We demonstrate the effectiveness of our framework through applications to various spatio-temporal systems, including fluid flows and global weather patterns. Although sparse measurements have limitations, our experiments reveal that they are sufficient to accurately forecast system dynamics over long time horizons. Furthermore, our results indicate that the performance of the proposed method remains robust across different sensor placement strategies, with further improvements as the number of sensors increases. This robustness underscores the flexibility of our architecture, particularly in real-world scenarios where sensor data is often sparse and unevenly distributed.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/a5d7dfe093ef6e45a69cc0d2ff16ffa818868e0e" target='_blank'>
-              Subspace tracking for online system identification
+          <td><a href="https://www.semanticscholar.org/paper/6349955a6ebfdaea6dccf7c5a37ca13c45dc5599" target='_blank'>
+              Forecasting High-dimensional Spatio-Temporal Systems from Sparse Measurements
               </a>
             </td>
           <td>
-            Andr'as Sasfi, A. Padoan, Ivan Markovsky, Florian Dorfler
+            Jialin Song, Zezheng Song, Pu Ren, N. Benjamin Erichson, Michael W. Mahoney, Xiaoye Li
           </td>
-          <td>2024-12-12</td>
-          <td>ArXiv</td>
+          <td>2024-11-28</td>
+          <td>Machine Learning: Science and Technology</td>
           <td>0</td>
-          <td>1</td>
+          <td>23</td>
         </tr>
 
-        <tr id="Prediction of Kelvin-Helmholtz instability (KHI) is crucial across various fields, requiring extensive high-fidelity data. However, experimental data are often sparse and noisy, while simulated data may lack credibility due to discrepancies with real-world configurations and parameters. This underscores the need for field reconstruction and parameter inference from sparse, noisy data, which constitutes inverse problems. Based on the physics-informed neural networks (PINNs), the KH-PINN framework is established in this work to solve the inverse problems of KHI flows. By incorporating the governing physical equations, KH-PINN reconstructs continuous flow fields and infer unknown transport parameters from sparse, noisy observed data. The 2D unsteady incompressible flows with both constant and variable densities are studied. To our knowledge, this is the first application of PINNs to unsteady incompressible flows with variable densities. To address the spatiotemporal multiscale issue and enhance the reconstruction accuracy of small-scale structures, the multiscale embedding (ME) strategy is adopted. To address the magnitude multiscale issue and enhance the reconstruction accuracy of small-magnitude velocities, which are critical for KHI problems, the small-velocity amplification (SVA) strategy is proposed. The results demonstrate that KH-PINN can accurately reconstruct the fields with complex, evolving vortices and infer unknown parameters across a broad range of Reynolds numbers. Additionally, the energy-decaying and entropy-increasing curves are accurately obtained. The effectiveness of ME and SVA is validated through comparative studies, and the anti-noise and few-shot learning capabilities of KH-PINN are also validated. The code for this work is available at https://github.com/CAME-THU/KH-PINN.">
+        <tr id="Many dynamical systems are difficult or impossible to model using high fidelity physics based models. Consequently, researchers are relying more on data driven models to make predictions and forecasts. Based on limited training data, machine learning models often deviate from the true system states over time and need to be continually updated as new measurements are taken using data assimilation. Classical data assimilation algorithms typically require knowledge of the measurement noise statistics which may be unknown. In this paper, we introduce a new data assimilation algorithm with a foundation in topological data analysis. By leveraging the differentiability of functions of persistence, gradient descent optimization is used to minimize topological differences between measurements and forecast predictions by tuning data driven model coefficients without using noise information from the measurements. We describe the method and focus on its capabilities performance using the chaotic Lorenz system as an example.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/ef49b25ebb936ec968b8484afa447714276f1d66" target='_blank'>
-              KH-PINN: Physics-informed neural networks for Kelvin-Helmholtz instability with spatiotemporal and magnitude multiscale
+          <td><a href="https://www.semanticscholar.org/paper/757a7fd89e8feada4c0a9c7066cb0b2020197b24" target='_blank'>
+              Topological Approach for Data Assimilation
               </a>
             </td>
           <td>
-            Jiahao Wu, Yuxin Wu, Xin Li, Guihua Zhang
+            Max M. Chumley, Firas A. Khasawneh
           </td>
           <td>2024-11-12</td>
           <td>ArXiv</td>
           <td>0</td>
+          <td>20</td>
+        </tr>
+
+        <tr id="Trajectory optimization is a widely used tool in the design and control of dynamical systems. Typically, not only nonlinear dynamics, but also couplings of the initial and final condition through implicit boundary constraints render the optimization problem non-convex. This paper investigates how the Koopman operator framework can be utilized to solve trajectory optimization problems in a (partially) convex fashion. While the Koopman operator has already been successfully employed in model predictive control, the challenge of addressing mixed boundary constraints within the Koopman framework has remained an open question. We first address this issue by explaining why a complete convexification of the problem is not possible. Secondly, we propose a method where we transform the trajectory optimization problem into a bilevel problem in which we are then able to convexify the high-dimensional lower-level problem. This separation yields a low-dimensional upper-level problem, which could be exploited in global optimization algorithms. Lastly, we demonstrate the effectiveness of the method on two example systems: the mathematical pendulum and the compass-gait walker.">
+          <td id="tag"><i class="material-icons">visibility_off</i></td>
+          <td><a href="https://www.semanticscholar.org/paper/5db0e4cbdd43eca7abb693a640841d350d2e707e" target='_blank'>
+              Koopman Based Trajectory Optimization with Mixed Boundaries
+              </a>
+            </td>
+          <td>
+            Mohamed Abou-Taleb, Maximilian Raff, Kathrin Flasskamp, C. D. Remy
+          </td>
+          <td>2024-12-04</td>
+          <td>ArXiv</td>
+          <td>0</td>
           <td>2</td>
         </tr>
 
-        <tr id="In this study, we apply two pillars of Scientific Machine Learning: Neural Ordinary Differential Equations (Neural ODEs) and Universal Differential Equations (UDEs) to the Lotka Volterra Predator Prey Model, a fundamental ecological model describing the dynamic interactions between predator and prey populations. The Lotka-Volterra model is critical for understanding ecological dynamics, population control, and species interactions, as it is represented by a system of differential equations. In this work, we aim to uncover the underlying differential equations without prior knowledge of the system, relying solely on training data and neural networks. Using robust modeling in the Julia programming language, we demonstrate that both Neural ODEs and UDEs can be effectively utilized for prediction and forecasting of the Lotka-Volterra system. More importantly, we introduce the forecasting breakdown point: the time at which forecasting fails for both Neural ODEs and UDEs. We observe how UDEs outperform Neural ODEs by effectively recovering the underlying dynamics and achieving accurate forecasting with significantly less training data. Additionally, we introduce Gaussian noise of varying magnitudes (from mild to high) to simulate real-world data perturbations and show that UDEs exhibit superior robustness, effectively recovering the underlying dynamics even in the presence of noisy data, while Neural ODEs struggle with high levels of noise. Through extensive hyperparameter optimization, we offer insights into neural network architectures, activation functions, and optimizers that yield the best results. This study opens the door to applying Scientific Machine Learning frameworks for forecasting tasks across a wide range of ecological and scientific domains.">
+        <tr id="The control of legged robots, particularly humanoid and quadruped robots, presents significant challenges due to their high-dimensional and nonlinear dynamics. While linear systems can be effectively controlled using methods like Model Predictive Control (MPC), the control of nonlinear systems remains complex. One promising solution is the Koopman Operator, which approximates nonlinear dynamics with a linear model, enabling the use of proven linear control techniques. However, achieving accurate linearization through data-driven methods is difficult due to issues like approximation error, domain shifts, and the limitations of fixed linear state-space representations. These challenges restrict the scalability of Koopman-based approaches. This paper addresses these challenges by proposing a continual learning algorithm designed to iteratively refine Koopman dynamics for high-dimensional legged robots. The key idea is to progressively expand the dataset and latent space dimension, enabling the learned Koopman dynamics to converge towards accurate approximations of the true system dynamics. Theoretical analysis shows that the linear approximation error of our method converges monotonically. Experimental results demonstrate that our method achieves high control performance on robots like Unitree G1/H1/A1/Go2 and ANYmal D, across various terrains using simple linear MPC controllers. This work is the first to successfully apply linearized Koopman dynamics for locomotion control of high-dimensional legged robots, enabling a scalable model-based control solution.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/851b83ce92820fa6d217f0d4cb4108121c1dd6d2" target='_blank'>
-              Scientific machine learning in ecological systems: A study on the predator-prey dynamics
+          <td><a href="https://www.semanticscholar.org/paper/504b4c1cb8478a275529cf00d6f4daef55c321aa" target='_blank'>
+              Continual Learning and Lifting of Koopman Dynamics for Linear Control of Legged Robots
               </a>
             </td>
           <td>
-            Ranabir Devgupta, R. Dandekar, R. Dandekar, S. Panat
+            Feihan Li, Abulikemu Abuduweili, Yifan Sun, Rui Chen, Weiye Zhao, Changliu Liu
           </td>
-          <td>2024-11-11</td>
+          <td>2024-11-21</td>
           <td>ArXiv</td>
+          <td>1</td>
+          <td>12</td>
+        </tr>
+
+        <tr id="Anticipating a tipping point, a transition from one stable steady state to another, is a problem of broad relevance due to the ubiquity of the phenomenon in diverse fields. The steady-state nature of the dynamics about a tipping point makes its prediction significantly more challenging than predicting other types of critical transitions from oscillatory or chaotic dynamics. Exploiting the benefits of noise, we develop a general data-driven and machine-learning approach to predicting potential future tipping in nonautonomous dynamical systems and validate the framework using examples from different fields. As an application, we address the problem of predicting the potential collapse of the Atlantic meridional overturning circulation, possibly driven by climate-induced changes in the freshwater input to the North Atlantic. Our predictions based on synthetic and currently available empirical data place a potential collapse window spanning from 2040 to 2065, in consistency with the results in the current literature.
+
+
+
+
+ Published by the American Physical Society
+ 2024
+
+
+">
+          <td id="tag"><i class="material-icons">visibility_off</i></td>
+          <td><a href="https://www.semanticscholar.org/paper/064ee1ad537ad72c8ec19d910f3e5c780d64429c" target='_blank'>
+              Machine learning prediction of tipping in complex dynamical systems
+              </a>
+            </td>
+          <td>
+            Shirin Panahi, Ling-Wei Kong, Mohammadamin Moradi, Zheng-Meng Zhai, Bryan Glaz, Mulugeta Haile, Ying-Cheng Lai
+          </td>
+          <td>2024-11-25</td>
+          <td>Physical Review Research</td>
           <td>0</td>
-          <td>3</td>
+          <td>10</td>
         </tr>
 
-        <tr id="The Koopman operator plays a crucial role in analyzing the global behavior of dynamical systems. Existing data-driven methods for approximating the Koopman operator or discovering the governing equations of the underlying system typically require a fixed set of basis functions, also called dictionary. The optimal choice of basis functions is highly problem-dependent and often requires domain knowledge. We present a novel gradient descent-based optimization framework for learning suitable and interpretable basis functions from data and show how it can be used in combination with EDMD, SINDy, and PDE-FIND. We illustrate the efficacy of the proposed approach with the aid of various benchmark problems such as the Ornstein-Uhlenbeck process, Chua's circuit, a nonlinear heat equation, as well as protein-folding data.">
+        <tr id="We propose a procedure for the numerical approximation of invariance equations arising in the moment matching technique associated with reduced-order modeling of high-dimensional dynamical systems. The Galerkin residual method is employed to find an approximate solution to the invariance equation using a Newton iteration on the coefficients of a monomial basis expansion of the solution. These solutions to the invariance equations can then be used to construct reduced-order models. We assess the ability of the method to solve the invariance PDE system as well as to achieve moment matching and recover a system's steady-state behaviour for linear and nonlinear signal generators with system dynamics up to $n=1000$ dimensions.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/074ff1387d4d32de316d495663c02b8f50f54d6f" target='_blank'>
-              Learning dynamical systems from data: Gradient-based dictionary optimization
+          <td><a href="https://www.semanticscholar.org/paper/ad6c6bc48c8661edae9afbfc939e6d991837f2f0" target='_blank'>
+              A polynomial approximation scheme for nonlinear model reduction by moment matching
               </a>
             </td>
           <td>
-            Mohammad Tabish, Neil K. Chada, Stefan Klus
+            Carlos Doebeli, Alessandro Astolfi, D. Kalise, Alessio Moreschini, G. Scarciotti, Joel D. Simard
           </td>
-          <td>2024-11-07</td>
+          <td>2024-12-17</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>19</td>
+          <td>20</td>
         </tr>
 
-        <tr id="In this paper, we present a new parametrization to perform direct data-driven analysis and controller synthesis for the error-in-variables case. To achieve this, we employ the Sherman-Morrison-Woodbury formula to transform the problem into a linear fractional transformation (LFT) with unknown measurement errors and disturbances as uncertainties. For bounded uncertainties, we apply robust control techniques to derive a guaranteed upper bound on the H2-norm of the unknown true system. To this end, a single semidefinite program (SDP) needs to be solved, with complexity that is independent of the amount of data. Furthermore, we exploit the signal-to-noise ratio to provide a data-dependent condition, that characterizes whether the proposed parametrization can be employed. The modular formulation allows to extend this framework to controller synthesis with different performance criteria, input-output settings, and various system properties. Finally, we validate the proposed approach through a numerical example.">
+        <tr id="This systematic review explores the theoretical foundations, evolution, applications, and future potential of Kolmogorov-Arnold Networks (KAN), a neural network model inspired by the Kolmogorov-Arnold representation theorem. KANs distinguish themselves from traditional neural networks by using learnable, spline-parameterized functions instead of fixed activation functions, allowing for flexible and interpretable representations of high-dimensional functions. This review details KAN's architectural strengths, including adaptive edge-based activation functions that improve parameter efficiency and scalability in applications such as time series forecasting, computational biomedicine, and graph learning. Key advancements, including Temporal-KAN, FastKAN, and Partial Differential Equation (PDE) KAN, illustrate KAN's growing applicability in dynamic environments, enhancing interpretability, computational efficiency, and adaptability for complex function approximation tasks. Additionally, this paper discusses KAN's integration with other architectures, such as convolutional, recurrent, and transformer-based models, showcasing its versatility in complementing established neural networks for tasks requiring hybrid approaches. Despite its strengths, KAN faces computational challenges in high-dimensional and noisy data settings, motivating ongoing research into optimization strategies, regularization techniques, and hybrid models. This paper highlights KAN's role in modern neural architectures and outlines future directions to improve its computational efficiency, interpretability, and scalability in data-intensive applications.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/de5b2106c1748e3318c926b97181ff89d1cf864c" target='_blank'>
-              A System Parametrization for Direct Data-Driven Analysis and Control with Error-in-Variables
+          <td><a href="https://www.semanticscholar.org/paper/87a18d71ac462a069801bc4472117d0abf8e5335" target='_blank'>
+              A Survey on Kolmogorov-Arnold Network
               </a>
             </td>
           <td>
-            Felix Brandle, Frank Allgower
+            Shriyank Somvanshi, Syed Aaqib Javed, Md Monzurul Islam, Diwas Pandit, Subasish Das
           </td>
-          <td>2024-11-11</td>
+          <td>2024-11-09</td>
+          <td>ArXiv</td>
+          <td>2</td>
+          <td>1</td>
+        </tr>
+
+        <tr id="Most model reduction methods are space-only in that they reduce the spatial dimension of the solution but not the temporal one. These methods integrate an encoding of the state of the nonlinear dynamical system forward in time. We propose a space-time method -- one that solves a system of algebraic equations for the encoding of the trajectory, i.e., the solution on a time interval $[0,T]$. The benefit of this approach is that with the same total number of degrees of freedom, a space-time encoding can leverage spatiotemporal correlations to represent the trajectory far more accurately than a space-only one. We use spectral proper orthogonal decomposition (SPOD) modes, a spatial basis at each temporal frequency tailored to the structures that appear at that frequency, to represent the trajectory. These modes have a number of properties that make them an ideal choice for space-time model reduction. We derive an algebraic system involving the SPOD coefficients that represent the solution, as well as the initial condition and the forcing. The online phase of the method consists of solving this system for the SPOD coefficients given the initial condition and forcing. We test the model on a Ginzburg-Landau system, a $1 + 1$ dimensional nonlinear PDE. We find that the proposed method is $\sim 2$ orders of magnitude more accurate than POD-Galerkin at the same number of modes and CPU time for all of our tests. In fact, the method is substantially more accurate even than the projection of the solution onto the POD modes, which is a lower bound for the error of any space-only Petrov-Galerkin method.">
+          <td id="tag"><i class="material-icons">visibility_off</i></td>
+          <td><a href="https://www.semanticscholar.org/paper/109eea0d8b80a6efaf7366912ea2c131eefd8e3f" target='_blank'>
+              Space-time model reduction in the frequency domain
+              </a>
+            </td>
+          <td>
+            PeterT. Frame, Aaron Towne
+          </td>
+          <td>2024-11-20</td>
           <td>ArXiv</td>
           <td>0</td>
           <td>2</td>
         </tr>
 
-        <tr id="Neural ODEs (NODEs) are continuous-time neural networks (NNs) that can process data without the limitation of time intervals. They have advantages in learning and understanding the evolution of complex real dynamics. Many previous works have focused on NODEs in concise forms, while numerous physical systems taking straightforward forms, in fact, belong to their more complex quasi-classes, thus appealing to a class of general NODEs with high scalability and flexibility to model those systems. This, however, may result in intricate nonlinear properties. In this paper, we introduce ControlSynth Neural ODEs (CSODEs). We show that despite their highly nonlinear nature, convergence can be guaranteed via tractable linear inequalities. In the composition of CSODEs, we introduce an extra control term for learning the potential simultaneous capture of dynamics at different scales, which could be particularly useful for partial differential equation-formulated systems. Finally, we compare several representative NNs with CSODEs on important physical dynamics under the inductive biases of CSODEs, and illustrate that CSODEs have better learning and predictive abilities in these settings.">
+        <tr id="Physics-Informed Neural Networks (PINNs) have emerged as a promising method for solving partial differential equations (PDEs) in scientific computing. While PINNs typically use multilayer perceptrons (MLPs) as their underlying architecture, recent advancements have explored alternative neural network structures. One such innovation is the Kolmogorov-Arnold Network (KAN), which has demonstrated benefits over traditional MLPs, including faster neural scaling and better interpretability. The application of KANs to physics-informed learning has led to the development of Physics-Informed KANs (PIKANs), enabling the use of KANs to solve PDEs. However, despite their advantages, KANs often suffer from slower training speeds, particularly in higher-dimensional problems where the number of collocation points grows exponentially with the dimensionality of the system. To address this challenge, we introduce Separable Physics-Informed Kolmogorov-Arnold Networks (SPIKANs). This novel architecture applies the principle of separation of variables to PIKANs, decomposing the problem such that each dimension is handled by an individual KAN. This approach drastically reduces the computational complexity of training without sacrificing accuracy, facilitating their application to higher-dimensional PDEs. Through a series of benchmark problems, we demonstrate the effectiveness of SPIKANs, showcasing their superior scalability and performance compared to PIKANs and highlighting their potential for solving complex, high-dimensional PDEs in scientific computing.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/43c2c16ec4f37600551f8be62e38d45212300a1e" target='_blank'>
-              ControlSynth Neural ODEs: Modeling Dynamical Systems with Guaranteed Convergence
+          <td><a href="https://www.semanticscholar.org/paper/cb7006c278ba49b0a4b7617ae7db6aeb79d96141" target='_blank'>
+              SPIKANs: Separable Physics-Informed Kolmogorov-Arnold Networks
               </a>
             </td>
           <td>
-            Wenjie Mei, Dongzhe Zheng, Shihua Li
+            Bruno Jacob, Amanda A. Howard, P. Stinis
           </td>
-          <td>2024-11-04</td>
+          <td>2024-11-09</td>
           <td>ArXiv</td>
           <td>1</td>
-          <td>1</td>
+          <td>14</td>
         </tr>
 
-        <tr id="We develop compositional learning algorithms for coupled dynamical systems. While deep learning has proven effective at modeling complex relationships from data, compositional couplings between system components typically introduce algebraic constraints on state variables, posing challenges to many existing data-driven approaches to modeling dynamical systems. Towards developing deep learning models for constrained dynamical systems, we introduce neural port-Hamiltonian differential algebraic equations (N-PHDAEs), which use neural networks to parametrize unknown terms in both the differential and algebraic components of a port-Hamiltonian DAE. To train these models, we propose an algorithm that uses automatic differentiation to perform index reduction, automatically transforming the neural DAE into an equivalent system of neural ordinary differential equations (N-ODEs), for which established model inference and backpropagation methods exist. The proposed compositional modeling framework and learning algorithms may be applied broadly to learn control-oriented models of dynamical systems in a variety of application areas, however, in this work, we focus on their application to the modeling of electrical networks. Experiments simulating the dynamics of nonlinear circuits exemplify the benefits of our approach: the proposed N-PHDAE model achieves an order of magnitude improvement in prediction accuracy and constraint satisfaction when compared to a baseline N-ODE over long prediction time horizons. We also validate the compositional capabilities of our approach through experiments on a simulated D.C. microgrid: we train individual N-PHDAE models for separate grid components, before coupling them to accurately predict the behavior of larger-scale networks.">
+        <tr id="We consider the problem of using experimental time-series data for parameter estimation in nonlinear ordinary differential equations, focusing on the case where the data is noisy, sparse, irregularly sampled, includes multiple experiments, and does not directly measure the system state or its time-derivative. To account for such low-quality data, we propose a new framework for gradient-based parameter estimation which uses the Picard operator to reformulate the problem as constrained optimization with infinite-dimensional variables and constraints. We then use the contractive properties of the Picard operator to propose a class of gradient-contractive algorithms and provide conditions under which such algorithms are guaranteed to converge to a local optima. The algorithms are then tested on a battery of models and variety of datasets in order to demonstrate robustness and improvement over alternative approaches.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/2388b39794f5824c68a3b768d02938b68a1c228a" target='_blank'>
-              Neural Port-Hamiltonian Differential Algebraic Equations for Compositional Learning of Electrical Networks
+          <td><a href="https://www.semanticscholar.org/paper/d81ee7733077c30ef583e9a222eb33a9f5e4178f" target='_blank'>
+              Picard Iteration for Parameter Estimation in Nonlinear Ordinary Differential Equations
               </a>
             </td>
           <td>
-            Cyrus Neary, Nathan Tsao, U. Topcu
+            Aleksandr Talitckii, Matthew M. Peet
           </td>
-          <td>2024-12-15</td>
+          <td>2024-12-28</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>49</td>
+          <td>4</td>
         </tr>
 
-        <tr id="
- Characterizing the nonlinear behavior of dynamical systems near the stability boundary is a critical step toward understanding, designing, and controlling systems prone to stability concerns. Traditional methods for bifurcation analysis in both experimental systems and large-dimensional models are often hindered either by the absence of an accurate model or by the analytical complexity involved. This paper presents a novel approach that combines the theoretical frameworks of nonlinear reduced-order modeling and stability analysis in dynamical systems with advanced machine learning techniques to perform bifurcation analysis in dynamical systems. By focusing on a low-dimensional nonlinear invariant manifold, this work proposes a data-driven methodology that simplifies the process of bifurcation analysis in dynamical systems. The core of our approach lies in utilizing carefully designed neural networks to identify nonlinear transformations that map observation space into reduced manifold coordinates in its normal form where bifurcation analysis can be performed. The unique integration of analytical and data-driven approaches in the proposed method enables the learning of these transformations and the performance of bifurcation analysis with a limited number of trajectories. Therefore, this approach improves bifurcation analysis in model-less experimental systems and cost-sensitive high-fidelity simulations. The effectiveness of this approach is demonstrated across several examples.">
+        <tr id="This paper develops a methodology for adaptive data-driven Model Predictive Control (MPC) using Koopman operators. While MPC is ubiquitous in various fields of engineering, the controller performance can deteriorate if the modeling error between the control model and the true dynamics persists, which may often be the case with complex nonlinear dynamics. Adaptive MPC techniques learn models online such that the controller can compensate for the modeling error by incorporating newly available data. We utilize the Koopman operator framework to formulate an adaptive MPC technique that corrects for model discrepancies in a computationally efficient manner by virtue of convex optimization. With the use of neural networks to learn embedding spaces, Koopman operator models enable accurate dynamics modeling. Such complex model forms, however, often lead to unstable online learning. To this end, the proposed method utilizes the soft update of target networks, a technique used in stabilization of model learning in Reinforcement Learning (RL). Also, we provide a discussion on which parameters to be chosen as online updated parameters based on a specific description of linear embedding models. Numerical simulations on a canonical nonlinear dynamical system show that the proposed method performs favorably compared to other data-driven MPC methods while achieving superior computational efficiency through the utilization of Koopman operators.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/3390fedb1047db4aa3bba8bfb0c549ae79e43689" target='_blank'>
-              Bifurcation analysis in dynamical systems through integration of machine learning and dynamical systems theory
+          <td><a href="https://www.semanticscholar.org/paper/22cfd9eeaa3083f566266ac7e18257b9d9c1474b" target='_blank'>
+              Model Predictive Control of Nonlinear Dynamics Using Online Adaptive Koopman Operators
               </a>
             </td>
           <td>
-            Nami Mogharabin, Amin Ghadami
+            Daisuke Uchida, Karthik Duraisamy
           </td>
-          <td>2024-11-27</td>
-          <td>Journal of Computational and Nonlinear Dynamics</td>
+          <td>2024-12-04</td>
+          <td>ArXiv</td>
           <td>0</td>
-          <td>2</td>
+          <td>3</td>
+        </tr>
+
+        <tr id="State-space models (SSMs) are a powerful statistical tool for modelling time-varying systems via a latent state. In these models, the latent state is never directly observed. Instead, a sequence of observations related to the state is available. The state-space model is defined by the state dynamics and the observation model, both of which are described by parametric distributions. Estimation of parameters of these distributions is a very challenging, but essential, task for performing inference and prediction. Furthermore, it is typical that not all states of the system interact. We can therefore encode the interaction of the states via a graph, usually not fully connected. However, most parameter estimation methods do not take advantage of this feature. In this work, we propose GraphGrad, a fully automatic approach for obtaining sparse estimates of the state interactions of a non-linear state-space model via a polynomial approximation. This novel methodology unveils the latent structure of the data-generating process, allowing us to infer both the structure and value of a rich and efficient parameterisation of a general state-space model. Our method utilises a differentiable particle filter to optimise a Monte Carlo likelihood estimator. It also promotes sparsity in the estimated system through the use of suitable proximity updates, known to be more efficient and stable than subgradient methods. As shown in our paper, a number of well-known dynamical systems can be accurately represented and recovered by our method, providing basis for application to real-world scenarios.">
+          <td id="tag"><i class="material-icons">visibility_off</i></td>
+          <td><a href="https://www.semanticscholar.org/paper/9a4c37d9e7064d49d3e9708586acebca148457d2" target='_blank'>
+              GraphGrad: Efficient Estimation of Sparse Polynomial Representations for General State-Space Models
+              </a>
+            </td>
+          <td>
+            Benjamin Cox, Émilie Chouzenoux, Víctor Elvira
+          </td>
+          <td>2024-11-23</td>
+          <td>ArXiv</td>
+          <td>0</td>
+          <td>3</td>
         </tr>
 
     </tbody>
@@ -1540,8 +1550,8 @@ <h3 id="recommended_articles">Recommended articles on <i>Symbolic regression</i>
   }
 
   var trace1 = {
-    x: ['2024'],
-    y: [3],
+    x: ['2024', '2025'],
+    y: [5, 0],
     name: 'Num of citations',
     yaxis: 'y1',
     type: 'scatter'
diff --git a/site/Time-series forecasting/index.html b/site/Time-series forecasting/index.html
index 91521e4e..a4ac4fe8 100644
--- a/site/Time-series forecasting/index.html	
+++ b/site/Time-series forecasting/index.html	
@@ -453,7 +453,7 @@ <h1>Time-series forecasting</h1>
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-12-30 06:05:36 UTC</i>
+  <i class="footer">This page was last updated on 2025-01-06 06:05:55 UTC</i>
   </p>
 
   <div class="note info" onclick="startIntro()">
@@ -537,7 +537,7 @@ <h3 id="manually_curated_articles">Manually curated articles on <i>Time-series f
             Xiang Zhang, M. Zeman, Theodoros Tsiligkaridis, M. Zitnik
           </td>
           <td>2021-10-11</td>
-          <td>ArXiv, International Conference on Learning Representations</td>
+          <td>International Conference on Learning Representations, ArXiv</td>
           <td>93</td>
           <td>48</td>
 
@@ -557,7 +557,7 @@ <h3 id="manually_curated_articles">Manually curated articles on <i>Time-series f
             Andrea Cini, Ivan Marisca, Daniele Zambon, C. Alippi
           </td>
           <td>2023-02-08</td>
-          <td>ArXiv, Neural Information Processing Systems</td>
+          <td>Neural Information Processing Systems, ArXiv</td>
           <td>24</td>
           <td>50</td>
 
@@ -597,7 +597,7 @@ <h3 id="manually_curated_articles">Manually curated articles on <i>Time-series f
             Andrea Cini, Ivan Marisca, Daniele Zambon, C. Alippi
           </td>
           <td>2023-10-24</td>
-          <td>ArXiv, arXiv.org</td>
+          <td>arXiv.org, ArXiv</td>
           <td>9</td>
           <td>50</td>
 
@@ -617,8 +617,8 @@ <h3 id="manually_curated_articles">Manually curated articles on <i>Time-series f
             Nate Gruver, Marc Finzi, Shikai Qiu, Andrew Gordon Wilson
           </td>
           <td>2023-10-11</td>
-          <td>ArXiv, Neural Information Processing Systems</td>
-          <td>214</td>
+          <td>Neural Information Processing Systems, ArXiv</td>
+          <td>213</td>
           <td>14</td>
 
             <td><a href='../recommendations/123acfbccca0460171b6b06a4012dbb991cde55b' target='_blank'>
@@ -637,7 +637,7 @@ <h3 id="manually_curated_articles">Manually curated articles on <i>Time-series f
             Chloe X. Wang, Oleksii Tsepa, Jun Ma, Bo Wang
           </td>
           <td>2024-02-01</td>
-          <td>ArXiv, arXiv.org</td>
+          <td>arXiv.org, ArXiv</td>
           <td>62</td>
           <td>5</td>
 
@@ -657,8 +657,8 @@ <h3 id="manually_curated_articles">Manually curated articles on <i>Time-series f
             Abhimanyu Das, Weihao Kong, Rajat Sen, Yichen Zhou
           </td>
           <td>2023-10-14</td>
-          <td>ArXiv, International Conference on Machine Learning</td>
-          <td>118</td>
+          <td>International Conference on Machine Learning, ArXiv</td>
+          <td>120</td>
           <td>14</td>
 
             <td><a href='../recommendations/f45f85fa1beaa795c24c4ff86f1f2deece72252f' target='_blank'>
@@ -677,8 +677,8 @@ <h3 id="manually_curated_articles">Manually curated articles on <i>Time-series f
             Gerald Woo, Chenghao Liu, Akshat Kumar, Caiming Xiong, Silvio Savarese, Doyen Sahoo
           </td>
           <td>2024-02-04</td>
-          <td>ArXiv, International Conference on Machine Learning</td>
-          <td>80</td>
+          <td>International Conference on Machine Learning, ArXiv</td>
+          <td>82</td>
           <td>25</td>
 
             <td><a href='../recommendations/4a111f7a3b56d0468f13104999844885157ef17d' target='_blank'>
@@ -697,8 +697,8 @@ <h3 id="manually_curated_articles">Manually curated articles on <i>Time-series f
             Ming Jin, Shiyu Wang, Lintao Ma, Zhixuan Chu, James Y. Zhang, X. Shi, Pin-Yu Chen, Yuxuan Liang, Yuan-Fang Li, Shirui Pan, Qingsong Wen
           </td>
           <td>2023-10-03</td>
-          <td>ArXiv, International Conference on Learning Representations</td>
-          <td>213</td>
+          <td>International Conference on Learning Representations, ArXiv</td>
+          <td>214</td>
           <td>9</td>
 
             <td><a href='../recommendations/16f01c1b3ddd0b2abd5ddfe4fdb3f74767607277' target='_blank'>
@@ -717,9 +717,9 @@ <h3 id="manually_curated_articles">Manually curated articles on <i>Time-series f
             Vijay Ekambaram, Arindam Jati, Nam H. Nguyen, Pankaj Dayama, Chandra Reddy, Wesley M. Gifford, Jayant Kalagnanam
           </td>
           <td>2024-01-08</td>
-          <td>ArXiv, arXiv.org</td>
+          <td>arXiv.org, ArXiv</td>
+          <td>4</td>
           <td>4</td>
-          <td>3</td>
 
             <td><a href='../recommendations/e2e1f1b8e6c1b7f4f166e15b7c674945856a51b6' target='_blank'>
               <i class="material-icons">open_in_new</i></a>
@@ -737,7 +737,7 @@ <h3 id="manually_curated_articles">Manually curated articles on <i>Time-series f
             Xiang Zhang, Ziyuan Zhao, Theodoros Tsiligkaridis, M. Zitnik
           </td>
           <td>2022-06-17</td>
-          <td>ArXiv, Neural Information Processing Systems</td>
+          <td>Neural Information Processing Systems, ArXiv</td>
           <td>223</td>
           <td>48</td>
 
@@ -757,8 +757,8 @@ <h3 id="manually_curated_articles">Manually curated articles on <i>Time-series f
             Huan He, Owen Queen, Teddy Koker, Consuelo Cuevas, Theodoros Tsiligkaridis, M. Zitnik
           </td>
           <td>2023-02-06</td>
-          <td>ArXiv, DBLP</td>
-          <td>42</td>
+          <td>DBLP, ArXiv</td>
+          <td>43</td>
           <td>48</td>
 
             <td><a href='../recommendations/5bd2c0acaf58c25f71617db2396188c74d29bf14' target='_blank'>
@@ -797,7 +797,7 @@ <h3 id="manually_curated_articles">Manually curated articles on <i>Time-series f
             Daniele Zambon, Andrea Cini, L. Livi, C. Alippi
           </td>
           <td>2023-01-04</td>
-          <td>ArXiv, arXiv.org</td>
+          <td>arXiv.org, ArXiv</td>
           <td>4</td>
           <td>50</td>
 
@@ -862,21 +862,6 @@ <h3 id="recommended_articles">Recommended articles on <i>Time-series forecasting
     </thead>
     <tbody>
 
-        <tr id="Time series foundation models have demonstrated strong performance in zero-shot learning, making them well-suited for predicting rapidly evolving patterns in real-world applications where relevant training data are scarce. However, most of these models rely on the Transformer architecture, which incurs quadratic complexity as input length increases. To address this, we introduce TSMamba, a linear-complexity foundation model for time series forecasting built on the Mamba architecture. The model captures temporal dependencies through both forward and backward Mamba encoders, achieving high prediction accuracy. To reduce reliance on large datasets and lower training costs, TSMamba employs a two-stage transfer learning process that leverages pretrained Mamba LLMs, allowing effective time series modeling with a moderate training set. In the first stage, the forward and backward backbones are optimized via patch-wise autoregressive prediction; in the second stage, the model trains a prediction head and refines other components for long-term forecasting. While the backbone assumes channel independence to manage varying channel numbers across datasets, a channel-wise compressed attention module is introduced to capture cross-channel dependencies during fine-tuning on specific multivariate datasets. Experiments show that TSMamba's zero-shot performance is comparable to state-of-the-art time series foundation models, despite using significantly less training data. It also achieves competitive or superior full-shot performance compared to task-specific prediction models. The code will be made publicly available.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/30abc3fad3c88886c189e216c8414b18c396c6bd" target='_blank'>
-              A Mamba Foundation Model for Time Series Forecasting
-              </a>
-            </td>
-          <td>
-            Haoyu Ma, Yushu Chen, Wenlai Zhao, Jinzhe Yang, Yingsheng Ji, Xinghua Xu, Xiaozhu Liu, Hao Jing, Shengzhuo Liu, Guangwen Yang
-          </td>
-          <td>2024-11-05</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>8</td>
-        </tr>
-
         <tr id="Accurately modeling and analyzing time series data is crucial for downstream applications across various fields, including healthcare, finance, astronomy, and epidemiology. However, real-world time series often exhibit irregularities such as misaligned timestamps, missing entries, and variable sampling rates, complicating their analysis. Existing approaches often rely on imputation, which can introduce biases. A few approaches that directly model irregularity tend to focus exclusively on either capturing intra-series patterns or inter-series relationships, missing the benefits of integrating both. To this end, we present WaveGNN, a novel framework designed to directly (i.e., no imputation) embed irregularly sampled multivariate time series data for accurate predictions. WaveGNN utilizes a Transformer-based encoder to capture intra-series patterns by directly encoding the temporal dynamics of each time series. To capture inter-series relationships, WaveGNN uses a dynamic graph neural network model, where each node represents a sensor, and the edges capture the long- and short-term relationships between them. Our experimental results on real-world healthcare datasets demonstrate that WaveGNN consistently outperforms existing state-of-the-art methods, with an average relative improvement of 14.7% in F1-score when compared to the second-best baseline in cases with extreme sparsity. Our ablation studies reveal that both intra-series and inter-series modeling significantly contribute to this notable improvement.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
           <td><a href="https://www.semanticscholar.org/paper/58504cccc55035221630bd35f09fb9db56f4f512" target='_blank'>
@@ -892,21 +877,6 @@ <h3 id="recommended_articles">Recommended articles on <i>Time-series forecasting
           <td>3</td>
         </tr>
 
-        <tr id="Time series forecasting remains a critical challenge across various domains, often complicated by high-dimensional data and long-term dependencies. This paper presents a novel transformer architecture for time series forecasting, incorporating two key innovations: parameter sharing (PS) and Spatial-Temporal Segment Attention (SegAtt). We also define the time series segment as the concatenation of sequence patches from the same positions across different variables. The proposed model, PSformer, reduces the number of training parameters through the parameter sharing mechanism, thereby improving model efficiency and scalability. The introduction of SegAtt could enhance the capability of capturing local spatio-temporal dependencies by computing attention over the segments, and improve global representation by integrating information across segments. The combination of parameter sharing and SegAtt significantly improves the forecasting performance. Extensive experiments on benchmark datasets demonstrate that PSformer outperforms popular baselines and other transformer-based approaches in terms of accuracy and scalability, establishing itself as an accurate and scalable tool for time series forecasting.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/496f3b7be63dc5765051593b2fe1ffd19782e3ea" target='_blank'>
-              PSformer: Parameter-efficient Transformer with Segment Attention for Time Series Forecasting
-              </a>
-            </td>
-          <td>
-            Yanlong Wang, Jian Xu, Fei Ma, Shao-Lun Huang, Danny D. Sun, Xiao-Ping Zhang
-          </td>
-          <td>2024-11-03</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>8</td>
-        </tr>
-
         <tr id="Transformer-based architectures have achieved unprecedented success in time series analysis. However, facing the challenge of across-domain modeling, existing studies utilize statistical prior as prompt engineering fails under the huge distribution shift among various domains. In this paper, a Unified Time Series Diffusion (UTSD) model is established for the first time to model the multi-domain probability distribution, utilizing the powerful probability distribution modeling ability of Diffusion. Unlike the autoregressive models that capture the conditional probabilities of the prediction horizon to the historical sequence, we use a diffusion denoising process to model the mixture distribution of the cross-domain data and generate the prediction sequence for the target domain directly utilizing conditional sampling. The proposed UTSD contains three pivotal designs: (1) The condition network captures the multi-scale fluctuation patterns from the observation sequence, which are utilized as context representations to guide the denoising network to generate the prediction sequence; (2) Adapter-based fine-tuning strategy, the multi-domain universal representation learned in the pretraining stage is utilized for downstream tasks in target domains; (3) The diffusion and denoising process on the actual sequence space, combined with the improved classifier free guidance as the conditional generation strategy, greatly improves the stability and accuracy of the downstream task. We conduct extensive experiments on mainstream benchmarks, and the pre-trained UTSD outperforms existing foundation models on all data domains, exhibiting superior zero-shot generalization ability. After training from scratch, UTSD achieves comparable performance against domain-specific proprietary models. The empirical results validate the potential of UTSD as a time series foundational model.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
           <td><a href="https://www.semanticscholar.org/paper/1a1b05bf5181bdcf2b1c93952567ef4290ee6ee9" target='_blank'>
@@ -982,36 +952,6 @@ <h3 id="recommended_articles">Recommended articles on <i>Time-series forecasting
           <td>3</td>
         </tr>
 
-        <tr id="Numerous industrial sectors necessitate models capable of providing robust forecasts across various horizons. Despite the recent strides in crafting specific architectures for time-series forecasting and developing pre-trained universal models, a comprehensive examination of their capability in accommodating varied-horizon forecasting during inference is still lacking. This paper bridges this gap through the design and evaluation of the Elastic Time-Series Transformer (ElasTST). The ElasTST model incorporates a non-autoregressive design with placeholders and structured self-attention masks, warranting future outputs that are invariant to adjustments in inference horizons. A tunable version of rotary position embedding is also integrated into ElasTST to capture time-series-specific periods and enhance adaptability to different horizons. Additionally, ElasTST employs a multi-scale patch design, effectively integrating both fine-grained and coarse-grained information. During the training phase, ElasTST uses a horizon reweighting strategy that approximates the effect of random sampling across multiple horizons with a single fixed horizon setting. Through comprehensive experiments and comparisons with state-of-the-art time-series architectures and contemporary foundation models, we demonstrate the efficacy of ElasTST's unique design elements. Our findings position ElasTST as a robust solution for the practical necessity of varied-horizon forecasting.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/1655d8b0d53bfdc28d81fbb6aa765118ac291460" target='_blank'>
-              ElasTST: Towards Robust Varied-Horizon Forecasting with Elastic Time-Series Transformer
-              </a>
-            </td>
-          <td>
-            Jiawen Zhang, Shun Zheng, Xumeng Wen, Xiaofang Zhou, Jiang Bian, Jia Li
-          </td>
-          <td>2024-11-04</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>8</td>
-        </tr>
-
-        <tr id="While numerous forecasters have been proposed using different network architectures, the Transformer-based models have state-of-the-art performance in time series forecasting. However, forecasters based on Transformers are still suffering from vulnerability to high-frequency signals, efficiency in computation, and bottleneck in full-spectrum utilization, which essentially are the cornerstones for accurately predicting time series with thousands of points. In this paper, we explore a novel perspective of enlightening signal processing for deep time series forecasting. Inspired by the filtering process, we introduce one simple yet effective network, namely FilterNet, built upon our proposed learnable frequency filters to extract key informative temporal patterns by selectively passing or attenuating certain components of time series signals. Concretely, we propose two kinds of learnable filters in the FilterNet: (i) Plain shaping filter, that adopts a universal frequency kernel for signal filtering and temporal modeling; (ii) Contextual shaping filter, that utilizes filtered frequencies examined in terms of its compatibility with input signals for dependency learning. Equipped with the two filters, FilterNet can approximately surrogate the linear and attention mappings widely adopted in time series literature, while enjoying superb abilities in handling high-frequency noises and utilizing the whole frequency spectrum that is beneficial for forecasting. Finally, we conduct extensive experiments on eight time series forecasting benchmarks, and experimental results have demonstrated our superior performance in terms of both effectiveness and efficiency compared with state-of-the-art methods. Code is available at this repository: https://github.com/aikunyi/FilterNet">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/3af83e96cc97a134738674d3167661ae710e5eb0" target='_blank'>
-              FilterNet: Harnessing Frequency Filters for Time Series Forecasting
-              </a>
-            </td>
-          <td>
-            Kun Yi, Jingru Fei, Qi Zhang, Hui He, Shufeng Hao, Defu Lian, Wei Fan
-          </td>
-          <td>2024-11-03</td>
-          <td>ArXiv</td>
-          <td>1</td>
-          <td>6</td>
-        </tr>
-
         <tr id="Irregularly sampled multivariate time series (ISMTS) are prevalent in reality. Due to their non-uniform intervals between successive observations and varying sampling rates among series, the channel-independent (CI) strategy, which has been demonstrated more desirable for complete multivariate time series forecasting in recent studies, has failed. This failure can be further attributed to the sampling sparsity, which provides insufficient information for effective CI learning, thereby reducing its capacity. When we resort to the channel-dependent (CD) strategy, even higher capacity cannot mitigate the potential loss of diversity in learning similar embedding patterns across different channels. We find that existing work considers CI and CD strategies to be mutually exclusive, primarily because they apply these strategies to the global channel. However, we hold the view that channel strategies do not necessarily have to be used globally. Instead, by appropriately applying them locally and globally, we can create an opportunity to take full advantage of both strategies. This leads us to introduce the Channel Harmony ISMTS Transformer (TimeCHEAT), which utilizes the CD locally and the CI globally. Specifically, we segment the ISMTS into sub-series level patches. Locally, the CD strategy aggregates information within each patch for time embedding learning, maximizing the use of relevant observations while reducing long-range irrelevant interference. Here, we enhance generality by transforming embedding learning into an edge weight prediction task using bipartite graphs, eliminating the need for special prior knowledge. Globally, the CI strategy is applied across patches, allowing the Transformer to learn individualized attention patterns for each channel. Experimental results indicate our proposed TimeCHEAT demonstrates competitive SOTA performance across three mainstream tasks.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
           <td><a href="https://www.semanticscholar.org/paper/89a442d354925c43b32c757f2fbce667c9ba0bc1" target='_blank'>
@@ -1042,6 +982,21 @@ <h3 id="recommended_articles">Recommended articles on <i>Time-series forecasting
           <td>3</td>
         </tr>
 
+        <tr id="In long-term time series forecasting, Transformer-based models have achieved great success, due to its ability to capture long-range dependencies. However, existing transformer-based methods face challenges in accurately identifying which variables play a pivotal role in the prediction process and tend to overemphasize noisy channels, thereby limiting the interpretability and practical effectiveness of the models. Besides, it faces scalability issues due to quadratic computational complexity of self-attention. In this paper, we propose a new model named Inverted Seasonal-Trend Decomposition Transformer (Ister), which addresses these challenges in long-term multivariate time series forecasting by designing an improved Transformer-based structure. Ister firstly decomposes original time series into seasonal and trend components. Then we propose a new Dot-attention mechanism to process the seasonal component, which improves both accuracy, computation complexity and interpretability. Upon completion of the training phase, it allows users to intuitively visualize the significance of each feature in the overall prediction. We conduct comprehensive experiments, and the results show that Ister achieves state-of-the-art (SOTA) performance on multiple datasets, surpassing existing models in long-term prediction tasks.">
+          <td id="tag"><i class="material-icons">visibility_off</i></td>
+          <td><a href="https://www.semanticscholar.org/paper/25edb19515621069aee3c7198b10055b9e13b615" target='_blank'>
+              Ister: Inverted Seasonal-Trend Decomposition Transformer for Explainable Multivariate Time Series Forecasting
+              </a>
+            </td>
+          <td>
+            Fanpu Cao, Shu Yang, Zhengjian Chen, Ye Liu, Laizhong Cui
+          </td>
+          <td>2024-12-25</td>
+          <td>ArXiv</td>
+          <td>0</td>
+          <td>0</td>
+        </tr>
+
         <tr id="Time series forecasting is crucial in many fields, yet current deep learning models struggle with noise, data sparsity, and capturing complex multi-scale patterns. This paper presents MFF-FTNet, a novel framework addressing these challenges by combining contrastive learning with multi-scale feature extraction across both frequency and time domains. MFF-FTNet introduces an adaptive noise augmentation strategy that adjusts scaling and shifting factors based on the statistical properties of the original time series data, enhancing model resilience to noise. The architecture is built around two complementary modules: a Frequency-Aware Contrastive Module (FACM) that refines spectral representations through frequency selection and contrastive learning, and a Complementary Time Domain Contrastive Module (CTCM) that captures both short- and long-term dependencies using multi-scale convolutions and feature fusion. A unified feature representation strategy enables robust contrastive learning across domains, creating an enriched framework for accurate forecasting. Extensive experiments on five real-world datasets demonstrate that MFF-FTNet significantly outperforms state-of-the-art models, achieving a 7.7% MSE improvement on multivariate tasks. These findings underscore MFF-FTNet's effectiveness in modeling complex temporal patterns and managing noise and sparsity, providing a comprehensive solution for both long- and short-term forecasting.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
           <td><a href="https://www.semanticscholar.org/paper/c6ceab16bfd7505012e83ee7a3e6c339f7cfe464" target='_blank'>
@@ -1117,21 +1072,6 @@ <h3 id="recommended_articles">Recommended articles on <i>Time-series forecasting
           <td>1</td>
         </tr>
 
-        <tr id="Time series analysis finds wide applications in fields such as weather forecasting, anomaly detection, and behavior recognition. Previous methods attempted to model temporal variations directly using 1D time series. However, this has been quite challenging due to the discrete nature of data points in time series and the complexity of periodic variation. In terms of periodicity, taking weather and traffic data as an example, there are multi-periodic variations such as yearly, monthly, weekly, and daily, etc. In order to break through the limitations of the previous methods, we decouple the implied complex periodic variations into inclusion and overlap relationships among different level periodic components based on the observation of the multi-periodicity therein and its inclusion relationships. This explicitly represents the naturally occurring pyramid-like properties in time series, where the top level is the original time series and lower levels consist of periodic components with gradually shorter periods, which we call the periodic pyramid. To further extract complex temporal variations, we introduce self-attention mechanism into the periodic pyramid, capturing complex periodic relationships by computing attention between periodic components based on their inclusion, overlap, and adjacency relationships. Our proposed Peri-midFormer demonstrates outstanding performance in five mainstream time series analysis tasks, including short- and long-term forecasting, imputation, classification, and anomaly detection.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/3303ceb65f24b62fe8ea3c73270e89d364a8f020" target='_blank'>
-              Peri-midFormer: Periodic Pyramid Transformer for Time Series Analysis
-              </a>
-            </td>
-          <td>
-            Qiang Wu, Gechang Yao, Zhixi Feng, Shu-zhen Yang
-          </td>
-          <td>2024-11-07</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>18</td>
-        </tr>
-
         <tr id="Time series forecasting is a crucial yet challenging task in machine learning, requiring domain-specific knowledge due to its wide-ranging applications. While recent Transformer models have improved forecasting capabilities, they come with high computational costs. Linear-based models have shown better accuracy than Transformers but still fall short of ideal performance. To address these challenges, we introduce the Decomposition State-Space Recurrent Neural Network (DSSRNN), a novel framework designed for both long-term and short-term time series forecasting. DSSRNN uniquely combines decomposition analysis to capture seasonal and trend components with state-space models and physics-based equations. We evaluate DSSRNN's performance on indoor air quality datasets, focusing on CO2 concentration prediction across various forecasting horizons. Results demonstrate that DSSRNN consistently outperforms state-of-the-art models, including transformer-based architectures, in terms of both Mean Squared Error (MSE) and Mean Absolute Error (MAE). For example, at the shortest horizon (T=96) in Office 1, DSSRNN achieved an MSE of 0.378 and an MAE of 0.401, significantly lower than competing models. Additionally, DSSRNN exhibits superior computational efficiency compared to more complex models. While not as lightweight as the DLinear model, DSSRNN achieves a balance between performance and efficiency, with only 0.11G MACs and 437MiB memory usage, and an inference time of 0.58ms for long-term forecasting. This work not only showcases DSSRNN's success but also establishes a new benchmark for physics-informed machine learning in environmental forecasting and potentially other domains.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
           <td><a href="https://www.semanticscholar.org/paper/2e885cde11c7135b8e6d899ec1309e7333f4c63e" target='_blank'>
@@ -1173,8 +1113,8 @@ <h3 id="recommended_articles">Recommended articles on <i>Time-series forecasting
           </td>
           <td>2024-11-24</td>
           <td>ArXiv</td>
-          <td>0</td>
-          <td>11</td>
+          <td>1</td>
+          <td>12</td>
         </tr>
 
         <tr id="Recent advancements in long-term time series forecasting (LTSF) have primarily focused on capturing cross-time and cross-variate (channel) dependencies within historical data. However, a critical aspect often overlooked by many existing methods is the explicit incorporation of \textbf{time-related features} (e.g., season, month, day of the week, hour, minute), which are essential components of time series data. The absence of this explicit time-related encoding limits the ability of current models to capture cyclical or seasonal trends and long-term dependencies, especially with limited historical input. To address this gap, we introduce a simple yet highly efficient module designed to encode time-related features, Time Stamp Forecaster (TimeSter), thereby enhancing the backbone's forecasting performance. By integrating TimeSter with a linear backbone, our model, TimeLinear, significantly improves the performance of a single linear projector, reducing MSE by an average of 23\% on benchmark datasets such as Electricity and Traffic. Notably, TimeLinear achieves these gains while maintaining exceptional computational efficiency, delivering results that are on par with or exceed state-of-the-art models, despite using a fraction of the parameters.">
@@ -1207,36 +1147,6 @@ <h3 id="recommended_articles">Recommended articles on <i>Time-series forecasting
           <td>1</td>
         </tr>
 
-        <tr id="Traditional time series forecasting models mainly rely on historical numeric values to predict future outcomes.While these models have shown promising results, they often overlook the rich information available in other modalities, such as textual descriptions of special events, which can provide crucial insights into future dynamics.However, research that jointly incorporates text in time series forecasting remains relatively underexplored compared to other cross-modality work. Additionally, the modality gap between time series data and textual information poses a challenge for multimodal learning. To address this task, we propose Text2Freq, a cross-modality model that integrates text and time series data via the frequency domain. Specifically, our approach aligns textual information to the low-frequency components of time series data, establishing more effective and interpretable alignments between these two modalities. Our experiments on paired datasets of real-world stock prices and synthetic texts show that Text2Freq achieves state-of-the-art performance, with its adaptable architecture encouraging future research in this field.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/6e8e966cd4f6a405d949fd9f8a41cb3b56da3d6d" target='_blank'>
-              Text2Freq: Learning Series Patterns from Text via Frequency Domain
-              </a>
-            </td>
-          <td>
-            Ming-Chih Lo, Ching Chang, Wenjie Peng
-          </td>
-          <td>2024-11-01</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>3</td>
-        </tr>
-
-        <tr id="In time-series analysis, many recent works seek to provide a unified view and representation for time-series across multiple domains, leading to the development of foundation models for time-series data. Despite diverse modeling techniques, existing models are black boxes and fail to provide insights and explanations about their representations. In this paper, we present VQShape, a pre-trained, generalizable, and interpretable model for time-series representation learning and classification. By introducing a novel representation for time-series data, we forge a connection between the latent space of VQShape and shape-level features. Using vector quantization, we show that time-series from different domains can be described using a unified set of low-dimensional codes, where each code can be represented as an abstracted shape in the time domain. On classification tasks, we show that the representations of VQShape can be utilized to build interpretable classifiers, achieving comparable performance to specialist models. Additionally, in zero-shot learning, VQShape and its codebook can generalize to previously unseen datasets and domains that are not included in the pre-training process. The code and pre-trained weights are available at https://github.com/YunshiWen/VQShape.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/9315a4c727616535e2f0afa87c3557ede7805722" target='_blank'>
-              Abstracted Shapes as Tokens - A Generalizable and Interpretable Model for Time-series Classification
-              </a>
-            </td>
-          <td>
-            Yunshi Wen, Tengfei Ma, Tsui-Wei Weng, Lam M. Nguyen, A. A. Julius
-          </td>
-          <td>2024-11-01</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>22</td>
-        </tr>
-
         <tr id="Accurate short-term energy consumption forecasting for commercial buildings is crucial for smart grid operations. While smart meters and deep learning models enable forecasting using past data from multiple buildings, data heterogeneity from diverse buildings can reduce model performance. The impact of increasing dataset heterogeneity in time series forecasting, while keeping size and model constant, is understudied. We tackle this issue using the ComStock dataset, which provides synthetic energy consumption data for U.S. commercial buildings. Two curated subsets, identical in size and region but differing in building type diversity, are used to assess the performance of various time series forecasting models, including fine-tuned open-source foundation models (FMs). The results show that dataset heterogeneity and model architecture have a greater impact on post-training forecasting performance than the parameter count. Moreover, despite the higher computational cost, fine-tuned FMs demonstrate competitive performance compared to base models trained from scratch.">
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           <td><a href="https://www.semanticscholar.org/paper/bc4f3ad82f4e6aaaf1843f2a91d4b640a3256749" target='_blank'>
@@ -1282,19 +1192,19 @@ <h3 id="recommended_articles">Recommended articles on <i>Time-series forecasting
           <td>19</td>
         </tr>
 
-        <tr id="Large language models (LLMs) have revolutionized natural language processing by achieving state-of-the-art performance across various tasks. Recently, their effectiveness as embedding models has gained attention, marking a paradigm shift from traditional encoder-only models like ELMo and BERT to decoder-only, large-scale LLMs such as GPT, LLaMA, and Mistral. This survey provides an in-depth overview of this transition, beginning with foundational techniques before the LLM era, followed by LLM-based embedding models through two main strategies to derive embeddings from LLMs. 1) Direct prompting: We mainly discuss the prompt designs and the underlying rationale for deriving competitive embeddings. 2) Data-centric tuning: We cover extensive aspects that affect tuning an embedding model, including model architecture, training objectives, data constructions, etc. Upon the above, we also cover advanced methods, such as handling longer texts, and multilingual and cross-modal data. Furthermore, we discuss factors affecting choices of embedding models, such as performance/efficiency comparisons, dense vs sparse embeddings, pooling strategies, and scaling law. Lastly, the survey highlights the limitations and challenges in adapting LLMs for embeddings, including cross-task embedding quality, trade-offs between efficiency and accuracy, low-resource, long-context, data bias, robustness, etc. This survey serves as a valuable resource for researchers and practitioners by synthesizing current advancements, highlighting key challenges, and offering a comprehensive framework for future work aimed at enhancing the effectiveness and efficiency of LLMs as embedding models.">
+        <tr id="Spatial-temporal forecasting has various applications in transportation, climate, and human activity domains. Current spatial-temporal forecasting models primarily adopt a macro perspective, focusing on achieving strong overall prediction performance for the entire system. However, most of these models overlook the importance of enhancing the uniformity of prediction performance across different nodes, leading to poor prediction capabilities for certain nodes and rendering some results impractical. This task is particularly challenging due to the inherent heterogeneity of spatial-temporal data. To address this issue, in this paper, we propose a novel Heterogeneity-informed Mixture-of-Experts (HiMoE) for fair spatial-temporal forecasting. Specifically, we design a Heterogeneity-Informed Graph Convolutional Network (HiGCN), integrated into each expert model to enhance the flexibility of the experts. To adapt to the heterogeneity of spatial-temporal data, we design a Node-wise Mixture-of-Experts (NMoE). This model decouples the spatial-temporal prediction task into sub-tasks at the spatial scale, which are then assigned to different experts. To allocate these sub-tasks, we use a mean-based graph decoupling method to distinguish the graph structure for each expert. The results are then aggregated using an output gating mechanism based on a dense Mixture-of-Experts (dMoE). Additionally, fairness-aware loss and evaluation functions are proposed to train the model with uniformity and accuracy as objectives. Experiments conducted on four datasets, encompassing diverse data types and spatial scopes, validate HiMoE's ability to scale across various real-world scenarios. Furthermore, HiMoE consistently outperforms baseline models, achieving superior performance in both accuracy and uniformity.">
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-          <td><a href="https://www.semanticscholar.org/paper/0a44db2f1035eedaba16b4d362437b3e6fe7ef26" target='_blank'>
-              LLMs are Also Effective Embedding Models: An In-depth Overview
+          <td><a href="https://www.semanticscholar.org/paper/f73419200ace34b8e505f2afab1206e01cca1075" target='_blank'>
+              HiMoE: Heterogeneity-Informed Mixture-of-Experts for Fair Spatial-Temporal Forecasting
               </a>
             </td>
           <td>
-            Chongyang Tao, Tao Shen, Shen Gao, Junshuo Zhang, Zhen Li, Zhengwei Tao, Shuai Ma
+            Shaohan Yu, Pan Deng, Yu Zhao, Junting Liu, Zi'ang Wang
           </td>
-          <td>2024-12-17</td>
+          <td>2024-11-30</td>
           <td>ArXiv</td>
-          <td>1</td>
-          <td>3</td>
+          <td>0</td>
+          <td>4</td>
         </tr>
 
         <tr id="Long-term time series forecasting (LTSF) involves predicting a large number of future values of a time series based on the past values and is an essential task in a wide range of domains including weather forecasting, stock market analysis, disease outbreak prediction. Over the decades LTSF algorithms have transitioned from statistical models to deep learning models like transformer models. Despite the complex architecture of transformer based LTSF models `Are Transformers Effective for Time Series Forecasting? (Zeng et al., 2023)' showed that simple linear models can outperform the state-of-the-art transformer based LTSF models. Recently, quantum machine learning (QML) is evolving as a domain to enhance the capabilities of classical machine learning models. In this paper we initiate the application of QML to LTSF problems by proposing QuLTSF, a simple hybrid QML model for multivariate LTSF. Through extensive experiments on a widely used weather dataset we show the advantages of QuLTSF over the state-of-the-art classical linear models, in terms of reduced mean squared error and mean absolute error.">
@@ -1312,36 +1222,6 @@ <h3 id="recommended_articles">Recommended articles on <i>Time-series forecasting
           <td>19</td>
         </tr>
 
-        <tr id="State Space Models (SSMs) are powerful tools for modeling sequential data in computer vision and time series analysis domains. However, traditional SSMs are limited by fixed, one-dimensional sequential processing, which restricts their ability to model non-local interactions in high-dimensional data. While methods like Mamba and VMamba introduce selective and flexible scanning strategies, they rely on predetermined paths, which fails to efficiently capture complex dependencies. We introduce Graph-Generating State Space Models (GG-SSMs), a novel framework that overcomes these limitations by dynamically constructing graphs based on feature relationships. Using Chazelle's Minimum Spanning Tree algorithm, GG-SSMs adapt to the inherent data structure, enabling robust feature propagation across dynamically generated graphs and efficiently modeling complex dependencies. We validate GG-SSMs on 11 diverse datasets, including event-based eye-tracking, ImageNet classification, optical flow estimation, and six time series datasets. GG-SSMs achieve state-of-the-art performance across all tasks, surpassing existing methods by significant margins. Specifically, GG-SSM attains a top-1 accuracy of 84.9% on ImageNet, outperforming prior SSMs by 1%, reducing the KITTI-15 error rate to 2.77%, and improving eye-tracking detection rates by up to 0.33% with fewer parameters. These results demonstrate that dynamic scanning based on feature relationships significantly improves SSMs' representational power and efficiency, offering a versatile tool for various applications in computer vision and beyond.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/805bbe0a1299e30ede6bf5d72172de5ae3140be9" target='_blank'>
-              GG-SSMs: Graph-Generating State Space Models
-              </a>
-            </td>
-          <td>
-            Nikola Zubic, Davide Scaramuzza
-          </td>
-          <td>2024-12-17</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>4</td>
-        </tr>
-
-        <tr id="Integrating multimodal Electronic Health Records (EHR) data, such as numerical time series and free-text clinical reports, has great potential in predicting clinical outcomes. However, prior work has primarily focused on capturing temporal interactions within individual samples and fusing multimodal information, overlooking critical temporal patterns across patients. These patterns, such as trends in vital signs like abnormal heart rate or blood pressure, can indicate deteriorating health or an impending critical event. Similarly, clinical notes often contain textual descriptions that reflect these patterns. Identifying corresponding temporal patterns across different modalities is crucial for improving the accuracy of clinical outcome predictions, yet it remains a challenging task. To address this gap, we introduce a Cross-Modal Temporal Pattern Discovery (CTPD) framework, designed to efficiently extract meaningful cross-modal temporal patterns from multimodal EHR data. Our approach introduces shared initial temporal pattern representations which are refined using slot attention to generate temporal semantic embeddings. To ensure rich cross-modal temporal semantics in the learned patterns, we introduce a contrastive-based TPNCE loss for cross-modal alignment, along with two reconstruction losses to retain core information of each modality. Evaluations on two clinically critical tasks, 48-hour in-hospital mortality and 24-hour phenotype classification, using the MIMIC-III database demonstrate the superiority of our method over existing approaches.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/396472357781a2d15b4122c0e3d7bd949e300216" target='_blank'>
-              CTPD: Cross-Modal Temporal Pattern Discovery for Enhanced Multimodal Electronic Health Records Analysis
-              </a>
-            </td>
-          <td>
-            Fuying Wang, Feng Wu, Yihan Tang, Lequan Yu
-          </td>
-          <td>2024-11-01</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>1</td>
-        </tr>
-
         <tr id="Time series data analysis is prevalent across various domains, including finance, healthcare, and environmental monitoring. Traditional time series clustering methods often struggle to capture the complex temporal dependencies inherent in such data. In this paper, we propose the Variational Mixture Graph Autoencoder (VMGAE), a graph-based approach for time series clustering that leverages the structural advantages of graphs to capture enriched data relationships and produces Gaussian mixture embeddings for improved separability. Comparisons with baseline methods are included with experimental results, demonstrating that our method significantly outperforms state-of-the-art time-series clustering techniques. We further validate our method on real-world financial data, highlighting its practical applications in finance. By uncovering community structures in stock markets, our method provides deeper insights into stock relationships, benefiting market prediction, portfolio optimization, and risk management.">
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           <td><a href="https://www.semanticscholar.org/paper/19c9d8206d35e476449b4339a28bf7a75530cb65" target='_blank'>
@@ -1394,7 +1274,7 @@ <h3 id="recommended_articles">Recommended articles on <i>Time-series forecasting
               </a>
             </td>
           <td>
-            Le Hoang Anh, Dang Thanh Vu, Seungmin Oh, Gwanghyun Yu, Nguyen Bui Ngoc Han, Hyoung‐Gook Kim, Jin-Sul Kim, Jin-Young Kim
+            L. Anh, D. Vu, Seungmin Oh, Gwanghyun Yu, Nguyen Bui Ngoc Han, Hyoung‐Gook Kim, Jin-Sul Kim, Jin-Young Kim
           </td>
           <td>2024-12-21</td>
           <td>Energies</td>
@@ -1417,6 +1297,21 @@ <h3 id="recommended_articles">Recommended articles on <i>Time-series forecasting
           <td>2</td>
         </tr>
 
+        <tr id="This work introduces the LLM Online Spatial-temporal Reconstruction (LLM-OSR) framework, which integrates Graph Signal Processing (GSP) and Large Language Models (LLMs) for online spatial-temporal signal reconstruction. The LLM-OSR utilizes a GSP-based spatial-temporal signal handler to enhance graph signals and employs LLMs to predict missing values based on spatiotemporal patterns. The performance of LLM-OSR is evaluated on traffic and meteorological datasets under varying Gaussian noise levels. Experimental results demonstrate that utilizing GPT-4-o mini within the LLM-OSR is accurate and robust under Gaussian noise conditions. The limitations are discussed along with future research insights, emphasizing the potential of combining GSP techniques with LLMs for solving spatiotemporal prediction tasks.">
+          <td id="tag"><i class="material-icons">visibility_off</i></td>
+          <td><a href="https://www.semanticscholar.org/paper/3d0723347ac5b9bfe25ab01caca3b01060b7238d" target='_blank'>
+              LLM Online Spatial-temporal Signal Reconstruction Under Noise
+              </a>
+            </td>
+          <td>
+            Yi Yan, Dayu Qin, E. Kuruoglu
+          </td>
+          <td>2024-11-24</td>
+          <td>ArXiv</td>
+          <td>0</td>
+          <td>26</td>
+        </tr>
+
         <tr id="Recently, the large amounts of time series data generated by IoT devices are used for forecasting. Various multivariate time series forecasting models have been developed using deep learning models. Among them, Transformer-based models, which can extract long-term dependencies within sequences, have attracted significant attention. However, it is necessary for Transformers to effectively capture dependencies between multiple time series data. Additionally, simplifying the structure is required for implementation on IoT devices, and there is also a need to develop models that mitigate the impact of noise present in time series data. In this paper, we propose a Transformer-based model called DDformer to address these challenges. DDformer is designed to effectively capture both temporal and spatial dependencies in time series data. It decomposes inputs into trend and seasonal components using decomposition layers and enhances the features of each time step and variable with dimension expansion/reduction layers. When validated on energy, financial, and weather datasets, DDformer reduced prediction error by up to 45.9% compared to the state-of-the-art model (FEDformer).">
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           <td><a href="https://www.semanticscholar.org/paper/9ae84613ff33176dfbb322c7af971ec08060582a" target='_blank'>
@@ -1447,21 +1342,6 @@ <h3 id="recommended_articles">Recommended articles on <i>Time-series forecasting
           <td>19</td>
         </tr>
 
-        <tr id="Due to the superior ability of global dependency, transformer and its variants have become the primary choice in Masked Time-series Modeling (MTM) towards time-series classification task. In this paper, we experimentally analyze that existing transformer-based MTM methods encounter with two under-explored issues when dealing with time series data: (1) they encode features by performing long-dependency ensemble averaging, which easily results in rank collapse and feature homogenization as the layer goes deeper; (2) they exhibit distinct priorities in fitting different frequency components contained in the time-series, inevitably leading to spectrum energy imbalance of encoded feature. To tackle these issues, we propose an auxiliary content-aware balanced decoder (CBD) to optimize the encoding quality in the spectrum space within masked modeling scheme. Specifically, the CBD iterates on a series of fundamental blocks, and thanks to two tailored units, each block could progressively refine the masked representation via adjusting the interaction pattern based on local content variations of time-series and learning to recalibrate the energy distribution across different frequency components. Moreover, a dual-constraint loss is devised to enhance the mutual optimization of vanilla decoder and our CBD. Extensive experimental results on ten time-series classification datasets show that our method nearly surpasses a bunch of baselines. Meanwhile, a series of explanatory results are showcased to sufficiently demystify the behaviors of our method.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/1edf401e4b8b3895581ebcc9399708785688527e" target='_blank'>
-              Content-aware Balanced Spectrum Encoding in Masked Modeling for Time Series Classification
-              </a>
-            </td>
-          <td>
-            Yudong Han, Haocong Wang, Yupeng Hu, Yongshun Gong, Xuemeng Song, Weili Guan
-          </td>
-          <td>2024-12-17</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>2</td>
-        </tr>
-
         <tr id="Long-term time-series forecasting is essential for planning and decision-making in economics, energy, and transportation, where long foresight is required. To obtain such long foresight, models must be both efficient and effective in processing long sequence. Recent advancements have enhanced the efficiency of these models; however, the challenge of effectively leveraging longer sequences persists. This is primarily due to the tendency of these models to overfit when presented with extended inputs, necessitating the use of shorter input lengths to maintain tolerable error margins. In this work, we investigate the multiscale modeling method and propose the Logsparse Decomposable Multiscaling (LDM) framework for the efficient and effective processing of long sequences. We demonstrate that by decoupling patterns at different scales in time series, we can enhance predictability by reducing non-stationarity, improve efficiency through a compact long input representation, and simplify the architecture by providing clear task assignments. Experimental results demonstrate that LDM not only outperforms all baselines in long-term forecasting benchmarks, but also reducing both training time and memory costs.">
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           <td><a href="https://www.semanticscholar.org/paper/c0f8b9239821e8634e3da203e4efd260ced23ca0" target='_blank'>
@@ -1507,6 +1387,111 @@ <h3 id="recommended_articles">Recommended articles on <i>Time-series forecasting
           <td>7</td>
         </tr>
 
+        <tr id="Temporal Graph Neural Networks (TGNNs) have emerged as powerful tools for modeling dynamic interactions across various domains. The design space of TGNNs is notably complex, given the unique challenges in runtime efficiency and scalability raised by the evolving nature of temporal graphs. We contend that many of the existing works on TGNN modeling inadequately explore the design space, leading to suboptimal designs. Viewing TGNN models through a performance-focused lens often obstructs a deeper understanding of the advantages and disadvantages of each technique. Specifically, benchmarking efforts inherently evaluate models in their original designs and implementations, resulting in unclear accuracy comparisons and misleading runtime. To address these shortcomings, we propose a practical comparative evaluation framework that performs a design space search across well-known TGNN modules based on a unified, optimized code implementation. Using our framework, we make the first efforts towards addressing three critical questions in TGNN design, spending over 10,000 GPU hours: (1) investigating the efficiency of TGNN module designs, (2) analyzing how the effectiveness of these modules correlates with dataset patterns, and (3) exploring the interplay between multiple modules. Key outcomes of this directed investigative approach include demonstrating that the most recent neighbor sampling and attention aggregator outperform uniform neighbor sampling and MLP-Mixer aggregator; Assessing static node memory as an effective node memory alternative, and showing that the choice between static or dynamic node memory should be based on the repetition patterns in the dataset. Our in-depth analysis of the interplay between TGNN modules and dataset patterns should provide a deeper insight into TGNN performance along with potential research directions for designing more general and effective TGNNs.">
+          <td id="tag"><i class="material-icons">visibility_off</i></td>
+          <td><a href="https://www.semanticscholar.org/paper/fb023ceece810fde0edc8d40d2f261a2fa5bb031" target='_blank'>
+              Towards Ideal Temporal Graph Neural Networks: Evaluations and Conclusions after 10,000 GPU Hours
+              </a>
+            </td>
+          <td>
+            Yuxin Yang, Hongkuan Zhou, Rajgopal Kannan, Viktor K. Prasanna
+          </td>
+          <td>2024-12-28</td>
+          <td>ArXiv</td>
+          <td>0</td>
+          <td>8</td>
+        </tr>
+
+        <tr id="Adapting Large Language Models (LLMs) that are extensively trained on abundant text data, and customizing the input prompt to enable time series forecasting has received considerable attention. While recent work has shown great potential for adapting the learned prior of LLMs, the formulation of the prompt to finetune LLMs remains challenging as prompt should be aligned with time series data. Additionally, current approaches do not effectively leverage word token embeddings which embody the rich representation space learned by LLMs. This emphasizes the need for a robust approach to formulate the prompt which utilizes the word token embeddings while effectively representing the characteristics of the time series. To address these challenges, we propose NNCL-TLLM: Nearest Neighbor Contrastive Learning for Time series forecasting via LLMs. First, we generate time series compatible text prototypes such that each text prototype represents both word token embeddings in its neighborhood and time series characteristics via end-to-end finetuning. Next, we draw inspiration from Nearest Neighbor Contrastive Learning to formulate the prompt while obtaining the top-$k$ nearest neighbor time series compatible text prototypes. We then fine-tune the layer normalization and positional embeddings of the LLM, keeping the other layers intact, reducing the trainable parameters and decreasing the computational cost. Our comprehensive experiments demonstrate that NNCL-TLLM outperforms in few-shot forecasting while achieving competitive or superior performance over the state-of-the-art methods in long-term and short-term forecasting tasks.">
+          <td id="tag"><i class="material-icons">visibility_off</i></td>
+          <td><a href="https://www.semanticscholar.org/paper/80aedaa1c23b162f861a42e21328a6850c767ad9" target='_blank'>
+              Rethinking Time Series Forecasting with LLMs via Nearest Neighbor Contrastive Learning
+              </a>
+            </td>
+          <td>
+            Jayanie Bogahawatte, Sachith Seneviratne, M. Perera, Saman K. Halgamuge
+          </td>
+          <td>2024-12-06</td>
+          <td>ArXiv</td>
+          <td>0</td>
+          <td>11</td>
+        </tr>
+
+        <tr id="Recent advancements in graph representation learning have shifted attention towards dynamic graphs, which exhibit evolving topologies and features over time. The increased use of such graphs creates a paramount need for generative models suitable for applications such as data augmentation, obfuscation, and anomaly detection. However, there are few generative techniques that handle continuously changing temporal graph data; existing work largely relies on augmenting static graphs with additional temporal information to model dynamic interactions between nodes. In this work, we propose a fundamentally different approach: We instead directly model interactions as a joint probability of an edge forming between two nodes at a given time. This allows us to autoregressively generate new synthetic dynamic graphs in a largely assumption free, scalable, and inductive manner. We formalize this approach as DG-Gen, a generative framework for continuous time dynamic graphs, and demonstrate its effectiveness over five datasets. Our experiments demonstrate that DG-Gen not only generates higher fidelity graphs compared to traditional methods but also significantly advances link prediction tasks.">
+          <td id="tag"><i class="material-icons">visibility_off</i></td>
+          <td><a href="https://www.semanticscholar.org/paper/5e1ec71f9cc9baaad41c71c4b7ad2bd20fa1c3f7" target='_blank'>
+              A Deep Probabilistic Framework for Continuous Time Dynamic Graph Generation
+              </a>
+            </td>
+          <td>
+            Ryien Hosseini, Filippo Simini, V. Vishwanath, Henry Hoffmann
+          </td>
+          <td>2024-12-20</td>
+          <td>ArXiv</td>
+          <td>0</td>
+          <td>32</td>
+        </tr>
+
+        <tr id="Traffic forecasting is an important problem in the operation and optimisation of transportation systems. State-of-the-art solutions train machine learning models by minimising the mean forecasting errors on the training data. The trained models often favour periodic events instead of aperiodic ones in their prediction results, as periodic events often prevail in the training data. While offering critical optimisation opportunities, aperiodic events such as traffic incidents may be missed by the existing models. To address this issue, we propose DualCast -- a model framework to enhance the learning capability of traffic forecasting models, especially for aperiodic events. DualCast takes a dual-branch architecture, to disentangle traffic signals into two types, one reflecting intrinsic {spatial-temporal} patterns and the other reflecting external environment contexts including aperiodic events. We further propose a cross-time attention mechanism, to capture high-order spatial-temporal relationships from both periodic and aperiodic patterns. DualCast is versatile. We integrate it with recent traffic forecasting models, consistently reducing their forecasting errors by up to 9.6% on multiple real datasets.">
+          <td id="tag"><i class="material-icons">visibility_off</i></td>
+          <td><a href="https://www.semanticscholar.org/paper/491db13bc65a23493ceb508adc0f63a5d623ac62" target='_blank'>
+              DualCast: Disentangling Aperiodic Events from Traffic Series with a Dual-Branch Model
+              </a>
+            </td>
+          <td>
+            Xinyu Su, Feng Liu, Yanchuan Chang, E. Tanin, Majid Sarvi, Jianzhong Qi
+          </td>
+          <td>2024-11-27</td>
+          <td>ArXiv</td>
+          <td>0</td>
+          <td>25</td>
+        </tr>
+
+        <tr id="How to best develop foundational models for time series forecasting remains an important open question. Tokenization is a crucial consideration in this effort: what is an effective discrete vocabulary for a real-valued sequential input? To address this question, we develop WaveToken, a wavelet-based tokenizer that allows models to learn complex representations directly in the space of time-localized frequencies. Our method first scales and decomposes the input time series, then thresholds and quantizes the wavelet coefficients, and finally pre-trains an autoregressive model to forecast coefficients for the forecast horizon. By decomposing coarse and fine structures in the inputs, wavelets provide an eloquent and compact language for time series forecasting that simplifies learning. Empirical results on a comprehensive benchmark, including 42 datasets for both in-domain and zero-shot settings, show that WaveToken: i) provides better accuracy than recently proposed foundation models for forecasting while using a much smaller vocabulary (1024 tokens), and performs on par or better than modern deep learning models trained specifically on each dataset; and ii) exhibits superior generalization capabilities, achieving the best average rank across all datasets for three complementary metrics. In addition, we show that our method can easily capture complex temporal patterns of practical relevance that are challenging for other recent pre-trained models, including trends, sparse spikes, and non-stationary time series with varying frequencies evolving over time.">
+          <td id="tag"><i class="material-icons">visibility_off</i></td>
+          <td><a href="https://www.semanticscholar.org/paper/6152808bf045e7ac7eb12bd3e91f4bb5129276b1" target='_blank'>
+              Enhancing Foundation Models for Time Series Forecasting via Wavelet-based Tokenization
+              </a>
+            </td>
+          <td>
+            Luca Masserano, Abdul Fatir Ansari, Boran Han, Xiyuan Zhang, Christos Faloutsos, Michael W. Mahoney, Andrew Gordon Wilson, Youngsuk Park, Syama Sundar Rangapuram, Danielle C. Maddix, Yuyang Wang
+          </td>
+          <td>2024-12-06</td>
+          <td>ArXiv</td>
+          <td>0</td>
+          <td>18</td>
+        </tr>
+
+        <tr id="Transformer-based models for time series forecasting (TSF) have attracted significant attention in recent years due to their effectiveness and versatility. However, these models often require extensive hyperparameter optimization (HPO) to achieve the best possible performance, and a unified pipeline for HPO in transformer-based TSF remains lacking. In this paper, we present one such pipeline and conduct extensive experiments on several state-of-the-art (SOTA) transformer-based TSF models. These experiments are conducted on standard benchmark datasets to evaluate and compare the performance of different models, generating practical insights and examples. Our pipeline is generalizable beyond transformer-based architectures and can be applied to other SOTA models, such as Mamba and TimeMixer, as demonstrated in our experiments. The goal of this work is to provide valuable guidance to both industry practitioners and academic researchers in efficiently identifying optimal hyperparameters suited to their specific domain applications. The code and complete experimental results are available on GitHub.">
+          <td id="tag"><i class="material-icons">visibility_off</i></td>
+          <td><a href="https://www.semanticscholar.org/paper/c4cbc92581791d004b3adf46dce82a363835dbb2" target='_blank'>
+              A Unified Hyperparameter Optimization Pipeline for Transformer-Based Time Series Forecasting Models
+              </a>
+            </td>
+          <td>
+            Jingjing Xu, Caesar Wu, , Grégoire Danoy, Pascal Bouvry
+          </td>
+          <td>2025-01-02</td>
+          <td>ArXiv</td>
+          <td>0</td>
+          <td>24</td>
+        </tr>
+
+        <tr id="Systems characterized by evolving interactions, prevalent in social, financial, and biological domains, are effectively modeled as continuous-time dynamic graphs (CTDGs). To manage the scale and complexity of these graph datasets, machine learning (ML) approaches have become essential. However, CTDGs pose challenges for ML because traditional static graph methods do not naturally account for event timings. Newer approaches, such as graph recurrent neural networks (GRNNs), are inherently time-aware and offer advantages over static methods for CTDGs. However, GRNNs face another issue: the short truncation of backpropagation-through-time (BPTT), whose impact has not been properly examined until now. In this work, we demonstrate that this truncation can limit the learning of dependencies beyond a single hop, resulting in reduced performance. Through experiments on a novel synthetic task and real-world datasets, we reveal a performance gap between full backpropagation-through-time (F-BPTT) and the truncated backpropagation-through-time (T-BPTT) commonly used to train GRNN models. We term this gap the"truncation gap"and argue that understanding and addressing it is essential as the importance of CTDGs grows, discussing potential future directions for research in this area.">
+          <td id="tag"><i class="material-icons">visibility_off</i></td>
+          <td><a href="https://www.semanticscholar.org/paper/e0f84770ce9af9483399afda07c4f67bb9acd9cf" target='_blank'>
+              Mind the truncation gap: challenges of learning on dynamic graphs with recurrent architectures
+              </a>
+            </td>
+          <td>
+            Joao Bravo, Jacopo Bono, Pedro Saleiro, Hugo Ferreira, P. Bizarro
+          </td>
+          <td>2024-12-30</td>
+          <td>ArXiv</td>
+          <td>0</td>
+          <td>18</td>
+        </tr>
+
     </tbody>
     <tfoot>
       <tr>
@@ -1536,8 +1521,8 @@ <h3 id="recommended_articles">Recommended articles on <i>Time-series forecasting
   }
 
   var trace1 = {
-    x: ['2024'],
-    y: [2],
+    x: ['2024', '2025'],
+    y: [1, 0],
     name: 'Num of citations',
     yaxis: 'y1',
     type: 'scatter'
diff --git a/site/recommendations/06a0ba437d41a7c82c08a9636a4438c1b5031378/index.html b/site/recommendations/06a0ba437d41a7c82c08a9636a4438c1b5031378/index.html
index 90fa91bd..7f6d77d8 100644
--- a/site/recommendations/06a0ba437d41a7c82c08a9636a4438c1b5031378/index.html
+++ b/site/recommendations/06a0ba437d41a7c82c08a9636a4438c1b5031378/index.html
@@ -445,7 +445,7 @@ <h1 id="_1"></h1>
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-12-30 06:05:43 UTC</i>
+  <i class="footer">This page was last updated on 2025-01-06 06:05:58 UTC</i>
   </p>
 
   <div class="note info" onclick="startIntro()">
@@ -544,7 +544,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2022-06-01</td>
           <td>Nonlinear Dynamics</td>
-          <td>31</td>
+          <td>32</td>
           <td>93</td>
         </tr>
 
diff --git a/site/recommendations/0acd117521ef5aafb09fed02ab415523b330b058/index.html b/site/recommendations/0acd117521ef5aafb09fed02ab415523b330b058/index.html
index ef906ffb..a5432646 100644
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+++ b/site/recommendations/0acd117521ef5aafb09fed02ab415523b330b058/index.html
@@ -445,7 +445,7 @@ <h1 id="_1"></h1>
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-12-30 06:05:46 UTC</i>
+  <i class="footer">This page was last updated on 2025-01-06 06:06:10 UTC</i>
   </p>
 
   <div class="note info" onclick="startIntro()">
@@ -508,7 +508,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2015-09-11</td>
           <td>Proceedings of the National Academy of Sciences</td>
-          <td>3476</td>
+          <td>3490</td>
           <td>68</td>
         </tr>
 
@@ -532,7 +532,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2020-05-05</td>
           <td>Nature Communications</td>
-          <td>301</td>
+          <td>305</td>
           <td>13</td>
         </tr>
 
diff --git a/site/recommendations/0d01d21137a5af9f04e4b16a55a0f732cb8a540b/index.html b/site/recommendations/0d01d21137a5af9f04e4b16a55a0f732cb8a540b/index.html
index 1efb7469..f3781803 100644
--- a/site/recommendations/0d01d21137a5af9f04e4b16a55a0f732cb8a540b/index.html
+++ b/site/recommendations/0d01d21137a5af9f04e4b16a55a0f732cb8a540b/index.html
@@ -445,7 +445,7 @@ <h1 id="_1"></h1>
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-12-30 06:05:19 UTC</i>
+  <i class="footer">This page was last updated on 2025-01-06 06:05:39 UTC</i>
   </p>
 
   <div class="note info" onclick="startIntro()">
diff --git a/site/recommendations/123acfbccca0460171b6b06a4012dbb991cde55b/index.html b/site/recommendations/123acfbccca0460171b6b06a4012dbb991cde55b/index.html
index 778077d8..1a3865a6 100644
--- a/site/recommendations/123acfbccca0460171b6b06a4012dbb991cde55b/index.html
+++ b/site/recommendations/123acfbccca0460171b6b06a4012dbb991cde55b/index.html
@@ -445,7 +445,7 @@ <h1 id="_1"></h1>
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-12-30 06:05:20 UTC</i>
+  <i class="footer">This page was last updated on 2025-01-06 06:05:40 UTC</i>
   </p>
 
   <div class="note info" onclick="startIntro()">
@@ -484,7 +484,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2024-03-12</td>
           <td>ArXiv</td>
-          <td>82</td>
+          <td>85</td>
           <td>18</td>
         </tr>
 
@@ -496,7 +496,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2024-02-04</td>
           <td>ArXiv</td>
-          <td>6</td>
+          <td>7</td>
           <td>67</td>
         </tr>
 
@@ -543,7 +543,7 @@ <h3 data-intro='Recommendations for the article'>
             Yong Liu, Haoran Zhang, Chenyu Li, Xiangdong Huang, Jianmin Wang, Mingsheng Long
           </td>
           <td>2024-02-04</td>
-          <td>ArXiv, DBLP</td>
+          <td>DBLP, ArXiv</td>
           <td>26</td>
           <td>67</td>
         </tr>
@@ -556,7 +556,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2023-10-05</td>
           <td>ArXiv</td>
-          <td>65</td>
+          <td>66</td>
           <td>5</td>
         </tr>
 
diff --git a/site/recommendations/16f01c1b3ddd0b2abd5ddfe4fdb3f74767607277/index.html b/site/recommendations/16f01c1b3ddd0b2abd5ddfe4fdb3f74767607277/index.html
index 20e27bde..5636bf02 100644
--- a/site/recommendations/16f01c1b3ddd0b2abd5ddfe4fdb3f74767607277/index.html
+++ b/site/recommendations/16f01c1b3ddd0b2abd5ddfe4fdb3f74767607277/index.html
@@ -445,7 +445,7 @@ <h1 id="_1"></h1>
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-12-30 06:05:24 UTC</i>
+  <i class="footer">This page was last updated on 2025-01-06 06:05:42 UTC</i>
   </p>
 
   <div class="note info" onclick="startIntro()">
@@ -520,7 +520,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2022-09-20</td>
           <td>IEEE Transactions on Knowledge and Data Engineering</td>
-          <td>90</td>
+          <td>91</td>
           <td>18</td>
         </tr>
 
@@ -544,7 +544,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2024-05-03</td>
           <td>ArXiv</td>
-          <td>13</td>
+          <td>14</td>
           <td>47</td>
         </tr>
 
diff --git a/site/recommendations/1df04f33a8ef313cc2067147dbb79c3ca7c5c99f/index.html b/site/recommendations/1df04f33a8ef313cc2067147dbb79c3ca7c5c99f/index.html
index 4d210c02..e5f0fd37 100644
--- a/site/recommendations/1df04f33a8ef313cc2067147dbb79c3ca7c5c99f/index.html
+++ b/site/recommendations/1df04f33a8ef313cc2067147dbb79c3ca7c5c99f/index.html
@@ -445,7 +445,7 @@ <h1 id="_1"></h1>
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-12-30 06:05:21 UTC</i>
+  <i class="footer">This page was last updated on 2025-01-06 06:05:41 UTC</i>
   </p>
 
   <div class="note info" onclick="startIntro()">
@@ -496,7 +496,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2024-02-13</td>
           <td>ArXiv, DBLP</td>
-          <td>43</td>
+          <td>42</td>
           <td>9</td>
         </tr>
 
@@ -520,7 +520,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2024-06-09</td>
           <td>ArXiv</td>
-          <td>4</td>
+          <td>5</td>
           <td>4</td>
         </tr>
 
diff --git a/site/recommendations/279cd637b7e38bba1dd8915b5ce68cbcacecbe68/index.html b/site/recommendations/279cd637b7e38bba1dd8915b5ce68cbcacecbe68/index.html
index c8d89706..5fbd8a6e 100644
--- a/site/recommendations/279cd637b7e38bba1dd8915b5ce68cbcacecbe68/index.html
+++ b/site/recommendations/279cd637b7e38bba1dd8915b5ce68cbcacecbe68/index.html
@@ -445,7 +445,7 @@ <h1 id="_1"></h1>
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-12-30 06:05:28 UTC</i>
+  <i class="footer">This page was last updated on 2025-01-06 06:05:45 UTC</i>
   </p>
 
   <div class="note info" onclick="startIntro()">
@@ -483,7 +483,7 @@ <h3 data-intro='Recommendations for the article'>
             Andreas Doerr, Christian Daniel, Martin Schiegg, D. Nguyen-Tuong, S. Schaal, Marc Toussaint, Sebastian Trimpe
           </td>
           <td>2018-01-31</td>
-          <td>ArXiv, DBLP, MAG</td>
+          <td>DBLP, ArXiv, MAG</td>
           <td>115</td>
           <td>93</td>
         </tr>
@@ -536,18 +536,6 @@ <h3 data-intro='Recommendations for the article'>
           <td>50</td>
         </tr>
 
-        <tr id="Forecasting the behaviour of complex dynamical systems such as interconnected sensor networks characterized by high-dimensional multivariate time series(MTS) is of paramount importance for making informed decisions and planning for the future in a broad spectrum of applications. Graph forecasting networks(GFNs) are well-suited for forecasting MTS data that exhibit spatio-temporal dependencies. However, most prior works of GFN-based methods on MTS forecasting rely on domain-expertise to model the nonlinear dynamics of the system, but neglect the potential to leverage the inherent relational-structural dependencies among time series variables underlying MTS data. On the other hand, contemporary works attempt to infer the relational structure of the complex dependencies between the variables and simultaneously learn the nonlinear dynamics of the interconnected system but neglect the possibility of incorporating domain-specific prior knowledge to improve forecast accuracy. To this end, we propose a hybrid architecture that combines explicit prior knowledge with implicit knowledge of the relational structure within the MTS data. It jointly learns intra-series temporal dependencies and inter-series spatial dependencies by encoding time-conditioned structural spatio-temporal inductive biases to provide more accurate and reliable forecasts. It also models the time-varying uncertainty of the multi-horizon forecasts to support decision-making by providing estimates of prediction uncertainty. The proposed architecture has shown promising results on multiple benchmark datasets and outperforms state-of-the-art forecasting methods by a significant margin. We report and discuss the ablation studies to validate our forecasting architecture.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/05cd3afc8208f1c0dd61b09a90f35dd42497e175" target='_blank'>Multi-Knowledge Fusion Network for Time Series Representation Learning</a></td>
-          <td>
-            Sakhinana Sagar Srinivas, Shivam Gupta, Krishna Sai Sudhir Aripirala, Venkataramana Runkana
-          </td>
-          <td>2024-08-22</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>3</td>
-        </tr>
-
         <tr id="Real-world dynamical systems often consist of multiple stochastic subsystems that interact with each other. Modeling and forecasting the behavior of such dynamics are generally not easy, due to the inherent hardness in understanding the complicated interactions and evolutions of their constituents. This paper introduces the relational state-space model (R-SSM), a sequential hierarchical latent variable model that makes use of graph neural networks (GNNs) to simulate the joint state transitions of multiple correlated objects. By letting GNNs cooperate with SSM, R-SSM provides a flexible way to incorporate relational information into the modeling of multi-object dynamics. We further suggest augmenting the model with normalizing flows instantiated for vertex-indexed random variables and propose two auxiliary contrastive objectives to facilitate the learning. The utility of R-SSM is empirically evaluated on synthetic and real time series datasets.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
           <td><a href="https://www.semanticscholar.org/paper/7a1e5377b08489c2969f73c56efc557e34f578e1" target='_blank'>Relational State-Space Model for Stochastic Multi-Object Systems</a></td>
@@ -560,16 +548,32 @@ <h3 data-intro='Recommendations for the article'>
           <td>61</td>
         </tr>
 
-        <tr id="Over the past few years, research on deep graph learning has shifted from static graphs to temporal graphs in response to real-world complex systems that exhibit dynamic behaviors. In practice, temporal graphs are formalized as an ordered sequence of static graph snapshots observed at discrete time points. Sequence models such as RNNs or Transformers have long been the predominant backbone networks for modeling such temporal graphs. Yet, despite the promising results, RNNs struggle with long-range dependencies, while transformers are burdened by quadratic computational complexity. Recently, state space models (SSMs), which are framed as discretized representations of an underlying continuous-time linear dynamical system, have garnered substantial attention and achieved breakthrough advancements in independent sequence modeling. In this work, we undertake a principled investigation that extends SSM theory to temporal graphs by integrating structural information into the online approximation objective via the adoption of a Laplacian regularization term. The emergent continuous-time system introduces novel algorithmic challenges, thereby necessitating our development of GraphSSM, a graph state space model for modeling the dynamics of temporal graphs. Extensive experimental results demonstrate the effectiveness of our GraphSSM framework across various temporal graph benchmarks.">
+        <tr id="Time series modeling is a well-established problem, which often requires that methods (1) expressively represent complicated dependencies, (2) forecast long horizons, and (3) efficiently train over long sequences. State-space models (SSMs) are classical models for time series, and prior works combine SSMs with deep learning layers for efficient sequence modeling. However, we find fundamental limitations with these prior approaches, proving their SSM representations cannot express autoregressive time series processes. We thus introduce SpaceTime, a new state-space time series architecture that improves all three criteria. For expressivity, we propose a new SSM parameterization based on the companion matrix -- a canonical representation for discrete-time processes -- which enables SpaceTime's SSM layers to learn desirable autoregressive processes. For long horizon forecasting, we introduce a"closed-loop"variation of the companion SSM, which enables SpaceTime to predict many future time-steps by generating its own layer-wise inputs. For efficient training and inference, we introduce an algorithm that reduces the memory and compute of a forward pass with the companion matrix. With sequence length $\ell$ and state-space size $d$, we go from $\tilde{O}(d \ell)$ na\"ively to $\tilde{O}(d + \ell)$. In experiments, our contributions lead to state-of-the-art results on extensive and diverse benchmarks, with best or second-best AUROC on 6 / 7 ECG and speech time series classification, and best MSE on 14 / 16 Informer forecasting tasks. Furthermore, we find SpaceTime (1) fits AR($p$) processes that prior deep SSMs fail on, (2) forecasts notably more accurately on longer horizons than prior state-of-the-art, and (3) speeds up training on real-world ETTh1 data by 73% and 80% relative wall-clock time over Transformers and LSTMs.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/919e5db29c7b7be4468b975eb4c0fa4a543165fc" target='_blank'>State Space Models on Temporal Graphs: A First-Principles Study</a></td>
+          <td><a href="https://www.semanticscholar.org/paper/a7d68b1702af08ce4dbbf2cd0b083e744ae5c6be" target='_blank'>Effectively Modeling Time Series with Simple Discrete State Spaces</a></td>
           <td>
-            Jintang Li, Ruofan Wu, Xinzhou Jin, Boqun Ma, Liang Chen, Zibin Zheng
+            Michael Zhang, Khaled Kamal Saab, Michael Poli, Tri Dao, Karan Goel, Christopher Ré
           </td>
-          <td>2024-06-03</td>
+          <td>2023-03-16</td>
           <td>ArXiv</td>
-          <td>2</td>
-          <td>12</td>
+          <td>37</td>
+          <td>46</td>
+        </tr>
+
+        <tr id="
+
+ Gaussian state space models have been used for decades as generative models of sequential data. They admit an intuitive probabilistic interpretation, have a simple functional form, and enjoy widespread adoption. We introduce a unified algorithm to efficiently learn a broad class of linear and non-linear state space models, including variants where the emission and transition distributions are modeled by deep neural networks. Our learning algorithm simultaneously learns a compiled inference network and the generative model, leveraging a structured variational approximation parameterized by recurrent neural networks to mimic the posterior distribution. We apply the learning algorithm to both synthetic and real-world datasets, demonstrating its scalability and versatility. We find that using the structured approximation to the posterior results in models with significantly higher held-out likelihood.
+
+">
+          <td id="tag"><i class="material-icons">visibility_off</i></td>
+          <td><a href="https://www.semanticscholar.org/paper/2af17f153e3fd71e15db9216b972aef222f46617" target='_blank'>Structured Inference Networks for Nonlinear State Space Models</a></td>
+          <td>
+            R. G. Krishnan, Uri Shalit, D. Sontag
+          </td>
+          <td>2016-09-30</td>
+          <td>DBLP, ArXiv, MAG</td>
+          <td>440</td>
+          <td>48</td>
         </tr>
 
   </tbody>
diff --git a/site/recommendations/2b2aa13d4959073f61ad70555bc8c7da7d116196/index.html b/site/recommendations/2b2aa13d4959073f61ad70555bc8c7da7d116196/index.html
index c5b72276..20ad759a 100644
--- a/site/recommendations/2b2aa13d4959073f61ad70555bc8c7da7d116196/index.html
+++ b/site/recommendations/2b2aa13d4959073f61ad70555bc8c7da7d116196/index.html
@@ -445,7 +445,7 @@ <h1 id="_1"></h1>
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-12-30 06:05:44 UTC</i>
+  <i class="footer">This page was last updated on 2025-01-06 06:05:59 UTC</i>
   </p>
 
   <div class="note info" onclick="startIntro()">
@@ -556,7 +556,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2020-07-02</td>
           <td>ArXiv</td>
-          <td>140</td>
+          <td>142</td>
           <td>23</td>
         </tr>
 
@@ -568,7 +568,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2020-03-17</td>
           <td>Autom.</td>
-          <td>18</td>
+          <td>19</td>
           <td>5</td>
         </tr>
 
@@ -593,7 +593,7 @@ <h3 data-intro='Recommendations for the article'>
           <td>2022-06-20</td>
           <td>Philosophical transactions. Series A, Mathematical, physical, and engineering sciences</td>
           <td>57</td>
-          <td>33</td>
+          <td>34</td>
         </tr>
 
   </tbody>
diff --git a/site/recommendations/35e2571c17246577e0bc1b9de57a314c3b60e220/index.html b/site/recommendations/35e2571c17246577e0bc1b9de57a314c3b60e220/index.html
index 11604363..a9e873ca 100644
--- a/site/recommendations/35e2571c17246577e0bc1b9de57a314c3b60e220/index.html
+++ b/site/recommendations/35e2571c17246577e0bc1b9de57a314c3b60e220/index.html
@@ -445,7 +445,7 @@ <h1 id="_1"></h1>
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-12-30 06:05:46 UTC</i>
+  <i class="footer">This page was last updated on 2025-01-06 06:06:00 UTC</i>
   </p>
 
   <div class="note info" onclick="startIntro()">
@@ -543,7 +543,7 @@ <h3 data-intro='Recommendations for the article'>
             Philipp Holl, V. Koltun, Nils Thuerey
           </td>
           <td>2021-09-30</td>
-          <td>ArXiv, DBLP</td>
+          <td>DBLP, ArXiv</td>
           <td>6</td>
           <td>106</td>
         </tr>
@@ -584,16 +584,16 @@ <h3 data-intro='Recommendations for the article'>
           <td>17</td>
         </tr>
 
-        <tr id="None">
+        <tr id="Big data is transforming scientific progress by enabling the discovery of novel models, enhancing existing frameworks, and facilitating precise uncertainty quantification, while advancements in scientific machine learning complement this by providing powerful tools to solve inverse problems to identify the complex systems where traditional methods falter due to sparse or noisy data. We introduce two innovative neural operator frameworks tailored for discovering hidden physics and identifying unknown system parameters from sparse measurements. The first framework integrates a popular neural operator, DeepONet, and a physics-informed neural network to capture the relationship between sparse data and the underlying physics, enabling the accurate discovery of a family of governing equations. The second framework focuses on system parameter identification, leveraging a DeepONet pre-trained on sparse sensor measurements to initialize a physics-constrained inverse model. Both frameworks excel in handling limited data and preserving physical consistency. Benchmarking on the Burgers' equation and reaction-diffusion system demonstrates state-of-the-art performance, achieving average $L_2$ errors of $\mathcal{O}(10^{-2})$ for hidden physics discovery and absolute errors of $\mathcal{O}(10^{-3})$ for parameter identification. These results underscore the frameworks' robustness, efficiency, and potential for solving complex scientific problems with minimal observational data.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/55be4b71d7c8366b0f095e769f4586ce664c7415" target='_blank'>Discovering conservation laws using optimal transport and manifold learning</a></td>
+          <td><a href="https://www.semanticscholar.org/paper/fac52e25998ecb2657489d5358e6d0ca9064f2f7" target='_blank'>Learning Hidden Physics and System Parameters with Deep Operator Networks</a></td>
           <td>
-            Peter Y. Lu, Rumen Dangovski, M. Soljavci'c
+            Vijay Kag, Dibakar Roy Sarkar, Birupaksha Pal, Somdatta Goswami
           </td>
-          <td>2022-08-31</td>
-          <td>Nature Communications</td>
-          <td>12</td>
-          <td>13</td>
+          <td>2024-12-06</td>
+          <td>ArXiv</td>
+          <td>0</td>
+          <td>0</td>
         </tr>
 
   </tbody>
diff --git a/site/recommendations/3c9961153493370500020c81527b3548c96f81e0/index.html b/site/recommendations/3c9961153493370500020c81527b3548c96f81e0/index.html
index 83e387f4..44876a36 100644
--- a/site/recommendations/3c9961153493370500020c81527b3548c96f81e0/index.html
+++ b/site/recommendations/3c9961153493370500020c81527b3548c96f81e0/index.html
@@ -445,7 +445,7 @@ <h1 id="_1"></h1>
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-12-30 06:05:39 UTC</i>
+  <i class="footer">This page was last updated on 2025-01-06 06:05:57 UTC</i>
   </p>
 
   <div class="note info" onclick="startIntro()">
@@ -484,7 +484,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2015-09-11</td>
           <td>Proceedings of the National Academy of Sciences</td>
-          <td>3476</td>
+          <td>3490</td>
           <td>68</td>
         </tr>
 
@@ -496,7 +496,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2020-05-05</td>
           <td>Nature Communications</td>
-          <td>301</td>
+          <td>305</td>
           <td>13</td>
         </tr>
 
diff --git a/site/recommendations/3df50e9b73cc2937dfd651f4c3344bc99b7ed3f2/index.html b/site/recommendations/3df50e9b73cc2937dfd651f4c3344bc99b7ed3f2/index.html
index ae7ee070..aae25fae 100644
--- a/site/recommendations/3df50e9b73cc2937dfd651f4c3344bc99b7ed3f2/index.html
+++ b/site/recommendations/3df50e9b73cc2937dfd651f4c3344bc99b7ed3f2/index.html
@@ -445,7 +445,7 @@ <h1 id="_1"></h1>
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-12-30 06:05:40 UTC</i>
+  <i class="footer">This page was last updated on 2025-01-06 06:05:57 UTC</i>
   </p>
 
   <div class="note info" onclick="startIntro()">
@@ -508,7 +508,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2022-01-13</td>
           <td>Proceedings of the Royal Society A</td>
-          <td>76</td>
+          <td>77</td>
           <td>68</td>
         </tr>
 
@@ -536,6 +536,18 @@ <h3 data-intro='Recommendations for the article'>
           <td>83</td>
         </tr>
 
+        <tr id="Many complex phenomena, from weather systems to heartbeat rhythm patterns, are effectively modeled as low-dimensional dynamical systems. Such systems may behave chaotically under certain conditions, and so the ability to detect chaos based on empirical measurement is an important step in characterizing and predicting these processes. Classifying a system as chaotic usually requires estimating its largest Lyapunov exponent, which quantifies the average rate of convergence or divergence of initially close trajectories in state space, and for which a positive value is generally accepted as an operational definition of chaos. Estimating the largest Lyapunov exponent from observations of a process is especially challenging in systems affected by dynamical noise, which is the case for many models of real-world processes, in particular models of biological systems. We describe a novel method for estimating the largest Lyapunov exponent from data, based on training Deep Learning models on synthetically generated trajectories, and demonstrate that this method yields accurate and noise-robust predictions given relatively short inputs and across a range of different dynamical systems. Our method is unique in that it can analyze tree-shaped data, a ubiquitous topology in biological settings, and specifically in dynamics over lineages of cells or organisms. We also characterize the types of input information extracted by our models for their predictions, allowing for a deeper understanding into the different ways by which chaos can be analyzed in different topologies.">
+          <td id="tag"><i class="material-icons">visibility_off</i></td>
+          <td><a href="https://www.semanticscholar.org/paper/9fb357e57624525f27224822502061cc8fb831e1" target='_blank'>Detecting chaos in lineage-trees: A deep learning approach</a></td>
+          <td>
+            H. Rappeport, Irit Levin Reisman, Naftali Tishby, N. Balaban
+          </td>
+          <td>2021-06-08</td>
+          <td>ArXiv</td>
+          <td>3</td>
+          <td>56</td>
+        </tr>
+
         <tr id="A generally applicable robust data-driven network modeling strategy offers rapid means to predict and control complex systems. We propose a universal method for data-driven modeling of complex nonlinear dynamics from time-resolved snapshot data without prior knowledge. Complex nonlinear dynamics govern many fields of science and engineering. Data-driven dynamic modeling often assumes a low-dimensional subspace or manifold for the state. We liberate ourselves from this assumption by proposing cluster-based network modeling (CNM) bridging machine learning, network science, and statistical physics. CNM describes short- and long-term behavior and is fully automatable, as it does not rely on application-specific knowledge. CNM is demonstrated for the Lorenz attractor, ECG heartbeat signals, Kolmogorov flow, and a high-dimensional actuated turbulent boundary layer. Even the notoriously difficult modeling benchmark of rare events in the Kolmogorov flow is solved. This automatable universal data-driven representation of complex nonlinear dynamics complements and expands network connectivity science and promises new fast-track avenues to understand, estimate, predict, and control complex systems in all scientific fields.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
           <td><a href="https://www.semanticscholar.org/paper/b0c3d159c14b0488299269c3fd62da3b9f608709" target='_blank'>Cluster-based network modeling—From snapshots to complex dynamical systems</a></td>
diff --git a/site/recommendations/455bfc515eb279cc09023faa1f78c6efb61224ba/index.html b/site/recommendations/455bfc515eb279cc09023faa1f78c6efb61224ba/index.html
index 3a17feaf..e39f6030 100644
--- a/site/recommendations/455bfc515eb279cc09023faa1f78c6efb61224ba/index.html
+++ b/site/recommendations/455bfc515eb279cc09023faa1f78c6efb61224ba/index.html
@@ -445,7 +445,7 @@ <h1 id="_1"></h1>
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-12-30 06:05:17 UTC</i>
+  <i class="footer">This page was last updated on 2025-01-06 06:05:37 UTC</i>
   </p>
 
   <div class="note info" onclick="startIntro()">
@@ -579,7 +579,7 @@ <h3 data-intro='Recommendations for the article'>
             Steven Cheng-Xian Li, Benjamin M Marlin
           </td>
           <td>2020-07-12</td>
-          <td>ArXiv, DBLP, MAG</td>
+          <td>MAG, ArXiv, DBLP</td>
           <td>55</td>
           <td>34</td>
         </tr>
diff --git a/site/recommendations/4971f9abd024e40fbbdff2e9492745b68a6bca01/index.html b/site/recommendations/4971f9abd024e40fbbdff2e9492745b68a6bca01/index.html
index 089546d1..d6952be8 100644
--- a/site/recommendations/4971f9abd024e40fbbdff2e9492745b68a6bca01/index.html
+++ b/site/recommendations/4971f9abd024e40fbbdff2e9492745b68a6bca01/index.html
@@ -445,7 +445,7 @@ <h1 id="_1"></h1>
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-12-30 06:05:44 UTC</i>
+  <i class="footer">This page was last updated on 2025-01-06 06:05:59 UTC</i>
   </p>
 
   <div class="note info" onclick="startIntro()">
@@ -485,7 +485,7 @@ <h3 data-intro='Recommendations for the article'>
           <td>2022-09-04</td>
           <td>Scientific Reports</td>
           <td>4</td>
-          <td>24</td>
+          <td>25</td>
         </tr>
 
         <tr id="Modern societies have an abundance of data yet good system models are rare. Unfortunately, many of the current system identification and machine learning techniques fail to generalize outside of the training set, producing models that violate basic physical laws. This work proposes a novel method for the Sparse Identification of Nonlinear Dynamics with Side Information (SINDy-SI). SINDy-SI is an iterative method that uses Sum-of-Squares (SOS) programming to learn optimally fitted models while guaranteeing that the learned model satisfies side information, such as symmetries and physical laws. Guided by the principle of Occam's razor, that the simplest or most regularized best fitted model is typically the superior choice, during each iteration SINDy-SI prunes the basis functions associated with small coefficients, yielding a sparse dynamical model upon termination. Through several numerical experiments we will show how the combination of side information constraints and sparse polynomial representation cultivates dynamical models that obey known physical laws while displaying impressive generalized performance beyond the training set.">
@@ -508,7 +508,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2021-11-12</td>
           <td>J. Open Source Softw.</td>
-          <td>124</td>
+          <td>125</td>
           <td>68</td>
         </tr>
 
@@ -521,7 +521,7 @@ <h3 data-intro='Recommendations for the article'>
           <td>2020-01-31</td>
           <td>IEEE Robotics and Automation Letters</td>
           <td>24</td>
-          <td>24</td>
+          <td>25</td>
         </tr>
 
         <tr id="None">
@@ -544,7 +544,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2022-11-10</td>
           <td>SSRN Electronic Journal</td>
-          <td>15</td>
+          <td>17</td>
           <td>33</td>
         </tr>
 
diff --git a/site/recommendations/4a111f7a3b56d0468f13104999844885157ef17d/index.html b/site/recommendations/4a111f7a3b56d0468f13104999844885157ef17d/index.html
index cc4da942..f1fcd9e8 100644
--- a/site/recommendations/4a111f7a3b56d0468f13104999844885157ef17d/index.html
+++ b/site/recommendations/4a111f7a3b56d0468f13104999844885157ef17d/index.html
@@ -445,7 +445,7 @@ <h1 id="_1"></h1>
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-12-30 06:05:23 UTC</i>
+  <i class="footer">This page was last updated on 2025-01-06 06:05:42 UTC</i>
   </p>
 
   <div class="note info" onclick="startIntro()">
@@ -520,7 +520,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2024-03-12</td>
           <td>ArXiv</td>
-          <td>82</td>
+          <td>85</td>
           <td>18</td>
         </tr>
 
@@ -531,7 +531,7 @@ <h3 data-intro='Recommendations for the article'>
             Yong Liu, Haoran Zhang, Chenyu Li, Xiangdong Huang, Jianmin Wang, Mingsheng Long
           </td>
           <td>2024-02-04</td>
-          <td>ArXiv, DBLP</td>
+          <td>DBLP, ArXiv</td>
           <td>26</td>
           <td>67</td>
         </tr>
@@ -544,7 +544,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2022-11-27</td>
           <td>ArXiv</td>
-          <td>777</td>
+          <td>784</td>
           <td>35</td>
         </tr>
 
diff --git a/site/recommendations/5bd2c0acaf58c25f71617db2396188c74d29bf14/index.html b/site/recommendations/5bd2c0acaf58c25f71617db2396188c74d29bf14/index.html
index 6ae7f239..8b89e653 100644
--- a/site/recommendations/5bd2c0acaf58c25f71617db2396188c74d29bf14/index.html
+++ b/site/recommendations/5bd2c0acaf58c25f71617db2396188c74d29bf14/index.html
@@ -445,7 +445,7 @@ <h1 id="_1"></h1>
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-12-30 06:05:27 UTC</i>
+  <i class="footer">This page was last updated on 2025-01-06 06:05:44 UTC</i>
   </p>
 
   <div class="note info" onclick="startIntro()">
@@ -508,7 +508,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2022-03-15</td>
           <td>ACM Transactions on Knowledge Discovery from Data</td>
-          <td>53</td>
+          <td>55</td>
           <td>40</td>
         </tr>
 
@@ -555,7 +555,7 @@ <h3 data-intro='Recommendations for the article'>
             Xiaoyong Jin, Youngsuk Park, Danielle C. Maddix, Bernie Wang, Xifeng Yan
           </td>
           <td>2021-02-13</td>
-          <td>ArXiv, DBLP</td>
+          <td>DBLP, ArXiv</td>
           <td>65</td>
           <td>66</td>
         </tr>
diff --git a/site/recommendations/5d150cec2775f9bc863760448f14104cc8f42368/index.html b/site/recommendations/5d150cec2775f9bc863760448f14104cc8f42368/index.html
index ad344ba9..4f1989a0 100644
--- a/site/recommendations/5d150cec2775f9bc863760448f14104cc8f42368/index.html
+++ b/site/recommendations/5d150cec2775f9bc863760448f14104cc8f42368/index.html
@@ -445,7 +445,7 @@ <h1 id="_1"></h1>
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-12-30 06:05:37 UTC</i>
+  <i class="footer">This page was last updated on 2025-01-06 06:05:56 UTC</i>
   </p>
 
   <div class="note info" onclick="startIntro()">
@@ -484,7 +484,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2019-03-29</td>
           <td>Proceedings of the National Academy of Sciences of the United States of America</td>
-          <td>661</td>
+          <td>662</td>
           <td>68</td>
         </tr>
 
@@ -520,7 +520,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2020-05-05</td>
           <td>Nature Communications</td>
-          <td>301</td>
+          <td>305</td>
           <td>13</td>
         </tr>
 
diff --git a/site/recommendations/60d0d998fa038182b3b69a57adb9b2f82d40589c/index.html b/site/recommendations/60d0d998fa038182b3b69a57adb9b2f82d40589c/index.html
index 356827ce..77122814 100644
--- a/site/recommendations/60d0d998fa038182b3b69a57adb9b2f82d40589c/index.html
+++ b/site/recommendations/60d0d998fa038182b3b69a57adb9b2f82d40589c/index.html
@@ -445,7 +445,7 @@ <h1 id="_1"></h1>
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-12-30 06:05:39 UTC</i>
+  <i class="footer">This page was last updated on 2025-01-06 06:05:56 UTC</i>
   </p>
 
   <div class="note info" onclick="startIntro()">
@@ -581,7 +581,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2020-01-13</td>
           <td>ArXiv</td>
-          <td>516</td>
+          <td>517</td>
           <td>26</td>
         </tr>
 
diff --git a/site/recommendations/648d90b713997a771e2c49f02cd771e8b7b10b37/index.html b/site/recommendations/648d90b713997a771e2c49f02cd771e8b7b10b37/index.html
index 414872b2..12e75391 100644
--- a/site/recommendations/648d90b713997a771e2c49f02cd771e8b7b10b37/index.html
+++ b/site/recommendations/648d90b713997a771e2c49f02cd771e8b7b10b37/index.html
@@ -445,7 +445,7 @@ <h1 id="_1"></h1>
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-12-30 06:05:26 UTC</i>
+  <i class="footer">This page was last updated on 2025-01-06 06:05:44 UTC</i>
   </p>
 
   <div class="note info" onclick="startIntro()">
@@ -544,7 +544,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2023-10-21</td>
           <td>ArXiv</td>
-          <td>33</td>
+          <td>34</td>
           <td>4</td>
         </tr>
 
diff --git a/site/recommendations/73dd9c49f205280991826b2ea4b50344203916b4/index.html b/site/recommendations/73dd9c49f205280991826b2ea4b50344203916b4/index.html
index e83f891c..ffa60d73 100644
--- a/site/recommendations/73dd9c49f205280991826b2ea4b50344203916b4/index.html
+++ b/site/recommendations/73dd9c49f205280991826b2ea4b50344203916b4/index.html
@@ -445,7 +445,7 @@ <h1 id="_1"></h1>
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-12-30 06:05:45 UTC</i>
+  <i class="footer">This page was last updated on 2025-01-06 06:05:59 UTC</i>
   </p>
 
   <div class="note info" onclick="startIntro()">
@@ -485,7 +485,7 @@ <h3 data-intro='Recommendations for the article'>
           <td>2022-09-04</td>
           <td>Scientific Reports</td>
           <td>4</td>
-          <td>24</td>
+          <td>25</td>
         </tr>
 
         <tr id="Data-driven modeling frameworks that adopt sparse regression techniques, such as sparse identification of nonlinear dynamics (SINDy) and its modifications, are developed to resolve difficulties in extracting underlying dynamics from experimental data. In contrast to neural-network-based methods, these methods are designed to obtain white-box analytical models. In this work, we incorporate the concept of SINDy and knowledge in the field of classical mechanics to identify interpretable and sparse expressions of total energy and the Lagrangian that shelters the hidden dynamics. Moreover, our method (hereafter referred as Lagrangian-SINDy) is developed to use knowledge of simple systems that form the system being analyzed to ensure the likelihood of correct results and to improve the learning pace. Lagrangian-SINDy is highly accurate in discovering interpretable dynamics via energy-related physical quantities. Its performance is validated with three popular multi-DOF nonlinear dynamical systems, namely the spherical pendulum, double pendulum and cart-pendulum system. Comparisons with other SINDy-based methods are made and Lagrangian-SINDy is found to provide the most compact analytical models.">
@@ -497,7 +497,7 @@ <h3 data-intro='Recommendations for the article'>
           <td>2020-01-31</td>
           <td>IEEE Robotics and Automation Letters</td>
           <td>24</td>
-          <td>24</td>
+          <td>25</td>
         </tr>
 
         <tr id="In this work we analyze the effectiveness of the Sparse Identification of Nonlinear Dynamics (SINDy) technique on three benchmark datasets for nonlinear identification, to provide a better understanding of its suitability when tackling real dynamical systems. While SINDy can be an appealing strategy for pursuing physics-based learning, our analysis highlights difficulties in dealing with unobserved states and non-smooth dynamics. Due to the ubiquity of these features in real systems in general, and control applications in particular, we complement our analysis with hands-on approaches to tackle these issues in order to exploit SINDy also in these challenging contexts.">
@@ -544,7 +544,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2017-11-15</td>
           <td>Proceedings. Mathematical, Physical, and Engineering Sciences</td>
-          <td>470</td>
+          <td>472</td>
           <td>68</td>
         </tr>
 
@@ -568,20 +568,20 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2020-04-05</td>
           <td>Proceedings. Mathematical, Physical, and Engineering Sciences</td>
-          <td>225</td>
+          <td>227</td>
           <td>68</td>
         </tr>
 
-        <tr id="Physics-based and first-principles models pervade the engineering and physical sciences, allowing for the ability to model the dynamics of complex systems with a prescribed accuracy. The approximations used in deriving governing equations often result in discrepancies between the model and sensor-based measurements of the system, revealing the approximate nature of the equations and/or the signal-to-noise ratio of the sensor itself. In modern dynamical systems, such discrepancies between model and measurement can lead to poor quantification, often undermining the ability to produce accurate and precise control algorithms. We introduce a discrepancy modeling framework to identify the missing physics and resolve the model-measurement mismatch with two distinct approaches: (i) by learning a model for the evolution of systematic state-space residual, and (ii) by discovering a model for the deterministic dynamical error. Regardless of approach, a common suite of data-driven model discovery methods can be used. The choice of method depends on one's intent (e.g., mechanistic interpretability) for discrepancy modeling, sensor measurement characteristics (e.g., quantity, quality, resolution), and constraints imposed by practical applications (e.g., modeling approaches using the suite of data-driven modeling methods on three continuous dynamical systems under varying signal-to-noise ratios. Finally, we emphasize structural shortcomings of each discrepancy modeling approach depending on error type. In summary, if the true dynamics are unknown (i.e., an imperfect model), one should learn a discrepancy model of the missing physics in the dynamical space. Yet, if the true dynamics are known yet model-measurement mismatch still exists, one should learn a discrepancy model in the state space.">
+        <tr id="We consider the problem of learning the dynamics of a linear system when one has access to data generated by an auxiliary system that shares similar (but not identical) dynamics, in addition to data from the true system. We use a weighted least squares approach, and provide finite sample error bounds of the learned model as a function of the number of samples and various system parameters from the two systems as well as the weight assigned to the auxiliary data. We show that the auxiliary data can help to reduce the intrinsic system identification error due to noise, at the price of adding a portion of error that is due to the differences between the two system models. We further provide a data-dependent bound that is computable when some prior knowledge about the systems, such as upper bounds on noise levels and model difference, is available. This bound can also be used to determine the weight that should be assigned to the auxiliary data during the model training stage.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/c4a38c94d23389326f5043d63b9f5f6f0d8c0c50" target='_blank'>Discrepancy Modeling Framework: Learning Missing Physics, Modeling Systematic Residuals, and Disambiguating between Deterministic and Random Effects</a></td>
+          <td><a href="https://www.semanticscholar.org/paper/f22b5a826ef61edb741f547b6e73999476cd695d" target='_blank'>Learning Dynamical Systems by Leveraging Data from Similar Systems</a></td>
           <td>
-            Megan R. Ebers, K. Steele, J. Kutz
+            Lei Xin, Lintao Ye, G. Chiu, S. Sundaram
           </td>
-          <td>2022-03-10</td>
-          <td>SIAM J. Appl. Dyn. Syst.</td>
-          <td>11</td>
-          <td>33</td>
+          <td>2023-02-08</td>
+          <td>ArXiv</td>
+          <td>7</td>
+          <td>37</td>
         </tr>
 
   </tbody>
diff --git a/site/recommendations/883547fdbd88552328a6615ec620f96e39c57018/index.html b/site/recommendations/883547fdbd88552328a6615ec620f96e39c57018/index.html
index 7d1254b5..b6d5aaca 100644
--- a/site/recommendations/883547fdbd88552328a6615ec620f96e39c57018/index.html
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 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-12-30 06:05:47 UTC</i>
+  <i class="footer">This page was last updated on 2025-01-06 06:06:10 UTC</i>
   </p>
 
   <div class="note info" onclick="startIntro()">
@@ -532,7 +532,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2020-04-05</td>
           <td>Proceedings. Mathematical, Physical, and Engineering Sciences</td>
-          <td>225</td>
+          <td>227</td>
           <td>68</td>
         </tr>
 
@@ -556,7 +556,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2015-09-11</td>
           <td>Proceedings of the National Academy of Sciences</td>
-          <td>3476</td>
+          <td>3490</td>
           <td>68</td>
         </tr>
 
@@ -572,16 +572,16 @@ <h3 data-intro='Recommendations for the article'>
           <td>0</td>
         </tr>
 
-        <tr id="We consider the data-driven discovery of governing equations from time-series data in the limit of high noise. The algorithms developed describe an extensive toolkit of methods for circumventing the deleterious effects of noise in the context of the <italic>sparse identification of nonlinear dynamics</italic> (SINDy) framework. We offer two primary contributions, both focused on noisy data acquired from a system <inline-formula> <tex-math notation="LaTeX">$\dot { \boldsymbol x} = { \boldsymbol f} ({ \boldsymbol x})$ </tex-math></inline-formula>. First, we propose, for use in high-noise settings, an extensive toolkit of critically enabling extensions for the SINDy regression method, to progressively cull functionals from an over-complete library and yield a set of sparse equations that regress to the derivate <inline-formula> <tex-math notation="LaTeX">$\dot { \boldsymbol {x}}$ </tex-math></inline-formula>. This toolkit includes: (regression step) weight timepoints based on estimated noise, use ensembles to estimate coefficients, and regress using FFTs; (culling step) leverage linear dependence of functionals, and restore and protect culled functionals based on Figures of Merit (FoMs). In a novel Assessment step, we define FoMs that compare model predictions to the original time-series (i.e., <inline-formula> <tex-math notation="LaTeX">${ \boldsymbol x}(t)$ </tex-math></inline-formula> rather than <inline-formula> <tex-math notation="LaTeX">$\dot { \boldsymbol {x}}(t)$ </tex-math></inline-formula>). These innovations can extract sparse governing equations and coefficients from high-noise time-series data (e.g., 300% added noise). For example, it discovers the correct sparse libraries in the Lorenz system, with median coefficient estimate errors equal to 1%−3% (for 50% noise), 6%−8% (for 100% noise), and 23%−25% (for 300% noise). The enabling modules in the toolkit are combined into a single method, but the individual modules can be tactically applied in other equation discovery methods (SINDy or not) to improve results on high-noise data. Second, we propose a technique, applicable to any model discovery method based on <inline-formula> <tex-math notation="LaTeX">$\dot { \boldsymbol x} = { \boldsymbol f} ({ \boldsymbol x})$ </tex-math></inline-formula>, to assess the accuracy of a discovered model in the context of non-unique solutions due to noisy data. Currently, this non-uniqueness can obscure a discovered model’s accuracy and thus a discovery method’s effectiveness. We describe a technique that uses linear dependencies among functionals to transform a discovered model into an equivalent form that is closest to the <italic>true</italic> model, enabling more accurate assessment of a discovered model’s correctness.">
+        <tr id="Active learning algorithms strategically select informative input samples, aiming to enhance understanding and optimize sample efficiency for dynamical systems. The efficacy of machine learning (ML) models with uncertainty quantification in identifying dynamical systems with different characteristics has not yet been explored. This paper investigates four ML models: Gaussian processes (GPs) with radial basis function (RBF), GPs with Matérn kernels, Bayesian neural networks (NNs) with Monte Carlo dropout(MCD), and ensemble neural networks (ENNs). Both continuous and non-continuous learning strategies are employed for all models. Five well known dynamical systems with different characteristics, state dimensionalities, and dynamical complexities are simulated to test the performance of the models along the metrics of test RMSE as well as samples and run time until convergence. Through systematic experimentation, this paper provides guidance for researchers selecting models and algorithms in active learning for system identification, with insights into their strengths and limitations. Gaussian Processes with RBF kernels are shown to be the best overall choice while ENNs with Bayesian inference emerge as a scalable alternative, showing promise for high-dimensional tasks. Employing continuous training has proven to enhance the performance of Gaussian processes with RBF kernels, as well as ENNs, resulting in significant improvements in both sample and run-time efficiency.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/a9803137946f0dc8997f23de925d5aec6e92dfb9" target='_blank'>A Toolkit for Data-Driven Discovery of Governing Equations in High-Noise Regimes</a></td>
+          <td><a href="https://www.semanticscholar.org/paper/4a3887d48d70464cf825d7d6d8834e36e77b5d04" target='_blank'>Comparative Analysis of Uncertainty Quantification Models in Active Learning for Efficient System Identification of Dynamical Systems</a></td>
           <td>
-            Charles B. Delahunt, J. Kutz
+            Hans Mertens, Frances Zhu
           </td>
-          <td>2021-11-08</td>
-          <td>IEEE Access</td>
-          <td>18</td>
-          <td>33</td>
+          <td>2024-08-28</td>
+          <td>2024 IEEE 20th International Conference on Automation Science and Engineering (CASE)</td>
+          <td>0</td>
+          <td>0</td>
         </tr>
 
   </tbody>
diff --git a/site/recommendations/b2eb064f432557c59ce99834d7dc7817e4687271/index.html b/site/recommendations/b2eb064f432557c59ce99834d7dc7817e4687271/index.html
index d9272fac..53fc6b02 100644
--- a/site/recommendations/b2eb064f432557c59ce99834d7dc7817e4687271/index.html
+++ b/site/recommendations/b2eb064f432557c59ce99834d7dc7817e4687271/index.html
@@ -445,7 +445,7 @@ <h1 id="_1"></h1>
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-12-30 06:05:42 UTC</i>
+  <i class="footer">This page was last updated on 2025-01-06 06:05:58 UTC</i>
   </p>
 
   <div class="note info" onclick="startIntro()">
@@ -509,7 +509,7 @@ <h3 data-intro='Recommendations for the article'>
           <td>2020-01-31</td>
           <td>IEEE Robotics and Automation Letters</td>
           <td>24</td>
-          <td>24</td>
+          <td>25</td>
         </tr>
 
         <tr id="System identification, the process of deriving mathematical models of dynamical systems from observed input-output data, has undergone a paradigm shift with the advent of learning-based methods. Addressing the intricate challenges of data-driven discovery in nonlinear dynamical systems, these methods have garnered significant attention. Among them, Sparse Identification of Nonlinear Dynamics (SINDy) has emerged as a transformative approach, distilling complex dynamical behaviors into interpretable linear combinations of basis functions. However, SINDy relies on domain-specific expertise to construct its foundational"library"of basis functions, which limits its adaptability and universality. In this work, we introduce a nonlinear system identification framework called LeARN that transcends the need for prior domain knowledge by learning the library of basis functions directly from data. To enhance adaptability to evolving system dynamics under varying noise conditions, we employ a novel meta-learning-based system identification approach that uses a lightweight deep neural network (DNN) to dynamically refine these basis functions. This not only captures intricate system behaviors but also adapts seamlessly to new dynamical regimes. We validate our framework on the Neural Fly dataset, showcasing its robust adaptation and generalization capabilities. Despite its simplicity, our LeARN achieves competitive dynamical error performance compared to SINDy. This work presents a step toward the autonomous discovery of dynamical systems, paving the way for a future where machine learning uncovers the governing principles of complex systems without requiring extensive domain-specific interventions.">
@@ -532,7 +532,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2020-04-05</td>
           <td>Proceedings. Mathematical, Physical, and Engineering Sciences</td>
-          <td>225</td>
+          <td>227</td>
           <td>68</td>
         </tr>
 
@@ -548,14 +548,14 @@ <h3 data-intro='Recommendations for the article'>
           <td>1</td>
         </tr>
 
-        <tr id="The sparse identification of nonlinear dynamics (SINDy) has been established as an effective technique to produce interpretable models of dynamical systems from time-resolved state data via sparse regression. However, to model parameterized systems, SINDy requires data from transient trajectories for various parameter values over the range of interest, which are typically difficult to acquire experimentally. In this work, we extend SINDy to be able to leverage data on fixed points and/or limit cycles to reduce the number of transient trajectories needed for successful system identification. To achieve this, we incorporate the data on these attractors at various parameter values as constraints in the optimization problem. First, we show that enforcing these as hard constraints leads to an ill-conditioned regression problem due to the large number of constraints. Instead, we implement soft constraints by modifying the cost function to be minimized. This leads to the formulation of a multi-objective sparse regression problem where we simultaneously seek to minimize the error of the fit to the transients trajectories and to the data on attractors, while penalizing the number of terms in the model. Our extension, demonstrated on several numerical examples, is more robust to noisy measurements and requires substantially less training data than the original SINDy method to correctly identify a parameterized dynamical system.">
+        <tr id="None">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
           <td><a href="https://www.semanticscholar.org/paper/0c03c126b4d641a81099470f03a7d5215a2a6820" target='_blank'>Multi-objective SINDy for parameterized model discovery from single transient trajectory data</a></td>
           <td>
             Javier A. Lemus, Benjamin Herrmann
           </td>
           <td>2024-05-14</td>
-          <td>ArXiv</td>
+          <td>Nonlinear Dynamics</td>
           <td>0</td>
           <td>0</td>
         </tr>
@@ -568,7 +568,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2015-09-11</td>
           <td>Proceedings of the National Academy of Sciences</td>
-          <td>3476</td>
+          <td>3490</td>
           <td>68</td>
         </tr>
 
@@ -580,7 +580,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2021-11-12</td>
           <td>J. Open Source Softw.</td>
-          <td>124</td>
+          <td>125</td>
           <td>68</td>
         </tr>
 
diff --git a/site/recommendations/c0fc3882a9976f6a9cdc3a724bce184b786503da/index.html b/site/recommendations/c0fc3882a9976f6a9cdc3a724bce184b786503da/index.html
index 58448e7f..2d959d17 100644
--- a/site/recommendations/c0fc3882a9976f6a9cdc3a724bce184b786503da/index.html
+++ b/site/recommendations/c0fc3882a9976f6a9cdc3a724bce184b786503da/index.html
@@ -445,7 +445,7 @@ <h1 id="_1"></h1>
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-12-30 06:05:48 UTC</i>
+  <i class="footer">This page was last updated on 2025-01-06 06:06:16 UTC</i>
   </p>
 
   <div class="note info" onclick="startIntro()">
@@ -496,7 +496,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2019-01-29</td>
           <td>ArXiv</td>
-          <td>48</td>
+          <td>49</td>
           <td>36</td>
         </tr>
 
diff --git a/site/recommendations/c3c94ccc094dcf546e8e31c9a42506302e837524/index.html b/site/recommendations/c3c94ccc094dcf546e8e31c9a42506302e837524/index.html
index dc4f7ed4..05e860ac 100644
--- a/site/recommendations/c3c94ccc094dcf546e8e31c9a42506302e837524/index.html
+++ b/site/recommendations/c3c94ccc094dcf546e8e31c9a42506302e837524/index.html
@@ -445,7 +445,7 @@ <h1 id="_1"></h1>
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-12-30 06:05:28 UTC</i>
+  <i class="footer">This page was last updated on 2025-01-06 06:05:45 UTC</i>
   </p>
 
   <div class="note info" onclick="startIntro()">
@@ -556,20 +556,20 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2022-02-17</td>
           <td>IEEE Transactions on Knowledge and Data Engineering</td>
-          <td>78</td>
+          <td>79</td>
           <td>44</td>
         </tr>
 
-        <tr id="Existing multivariate time series anomaly detection methods utilize graph neural networks to model inter-sensor dependencies and achieve satisfactory results. However, these methods often employ a predefined or self-learning static adjacency matrix for graph information aggregation, disregarding the dynamic characteristics of inter-sensor dependencies in the real world, which change over time and are observable at different time scales as dynamic changing graph structure information. Furthermore, existing techniques struggle to capture long-term temporal contextual relationships. To address these issues, we propose a Dynamic Graph Learning with Long and Short-term time model (DGL-LS) for multivariate time series anomaly detection. The network integrates a dynamic graph structure learning method among sensors in multi-time mode and long- and short-term temporal context information to enhance the prediction of multivariate time series anomalies. We propose a strategy for learning dynamic graphs that aggregates sensor node representations at various time intervals, and then uses an attention-based gating unit to evolve the node dynamic characterization and construct a series of adjacency matrices that describe the dynamic changes in graph structure over time. Moreover, we formulate a long-short time convolution to capture the long-term and short-term temporal dependencies within the time series. We demonstrate the superiority of our approach over other state-of-the-art methods by conducting extensive experiments on three publicly available datasets.">
+        <tr id="The online prediction of multivariate signals, existing simultaneously in space and time, from noisy partial observations is a fundamental task in numerous applications. We propose an efficient Neural Network architecture for the online estimation of time-varying graph signals named the Adaptive Least Mean Squares Graph Neural Networks (LMS-GNN). LMS-GNN aims to capture the time variation and bridge the cross-space-time interactions under the condition that signals are corrupted by noise and missing values. The LMS-GNN is a combination of adaptive graph filters and Graph Neural Networks (GNN). At each time step, the forward propagation of LMS-GNN is similar to adaptive graph filters where the output is based on the error between the observation and the prediction similar to GNN. The filter coefficients are updated via backpropagation as in GNN. Experimenting on real-world temperature data reveals that our LMS-GNN achieves more accurate online predictions compared to graph-based methods like adaptive graph filters and graph convolutional neural networks.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/379f54e4519d51a31de25e26fa651b3bd21d6530" target='_blank'>Dynamic Graph Learning with Long and Short-Term for Multivariate Time Series Anomaly Detection</a></td>
+          <td><a href="https://www.semanticscholar.org/paper/a03d0f3fd814c3732704bc65e2e60d0a92b0e8ae" target='_blank'>Adaptive Least Mean Squares Graph Neural Networks and Online Graph Signal Estimation</a></td>
           <td>
-            Yuyin Tian, Rong Gao, Lingyu Yan, Donghua Liu, Zhiwei Ye
+            Yi Yan, Changran Peng, E. Kuruoglu
           </td>
-          <td>2023-09-07</td>
-          <td>2023 IEEE 12th International Conference on Intelligent Data Acquisition and Advanced Computing Systems: Technology and Applications (IDAACS)</td>
-          <td>0</td>
-          <td>4</td>
+          <td>2024-01-27</td>
+          <td>ArXiv</td>
+          <td>1</td>
+          <td>26</td>
         </tr>
 
   </tbody>
diff --git a/site/recommendations/ccea298edb788edf821aef58f0952c3e8debc25a/index.html b/site/recommendations/ccea298edb788edf821aef58f0952c3e8debc25a/index.html
index bcfb6168..748f5448 100644
--- a/site/recommendations/ccea298edb788edf821aef58f0952c3e8debc25a/index.html
+++ b/site/recommendations/ccea298edb788edf821aef58f0952c3e8debc25a/index.html
@@ -445,7 +445,7 @@ <h1 id="_1"></h1>
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-12-30 06:05:19 UTC</i>
+  <i class="footer">This page was last updated on 2025-01-06 06:05:39 UTC</i>
   </p>
 
   <div class="note info" onclick="startIntro()">
@@ -532,7 +532,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2020-05-24</td>
           <td>Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining</td>
-          <td>1142</td>
+          <td>1149</td>
           <td>57</td>
         </tr>
 
diff --git a/site/recommendations/d3dbbd0f0de51b421a6220bd6480b8d2e99a88e9/index.html b/site/recommendations/d3dbbd0f0de51b421a6220bd6480b8d2e99a88e9/index.html
index a8194ad0..4140cc9d 100644
--- a/site/recommendations/d3dbbd0f0de51b421a6220bd6480b8d2e99a88e9/index.html
+++ b/site/recommendations/d3dbbd0f0de51b421a6220bd6480b8d2e99a88e9/index.html
@@ -445,7 +445,7 @@ <h1 id="_1"></h1>
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-12-30 06:05:16 UTC</i>
+  <i class="footer">This page was last updated on 2025-01-06 06:05:37 UTC</i>
   </p>
 
   <div class="note info" onclick="startIntro()">
diff --git a/site/recommendations/e2a83369383aff37224170c1ae3d3870d5d9e419/index.html b/site/recommendations/e2a83369383aff37224170c1ae3d3870d5d9e419/index.html
index 34a82ce6..3c476b00 100644
--- a/site/recommendations/e2a83369383aff37224170c1ae3d3870d5d9e419/index.html
+++ b/site/recommendations/e2a83369383aff37224170c1ae3d3870d5d9e419/index.html
@@ -445,7 +445,7 @@ <h1 id="_1"></h1>
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-12-30 06:05:18 UTC</i>
+  <i class="footer">This page was last updated on 2025-01-06 06:05:38 UTC</i>
   </p>
 
   <div class="note info" onclick="startIntro()">
diff --git a/site/recommendations/e2e1f1b8e6c1b7f4f166e15b7c674945856a51b6/index.html b/site/recommendations/e2e1f1b8e6c1b7f4f166e15b7c674945856a51b6/index.html
index 3bb981d1..15cf82f8 100644
--- a/site/recommendations/e2e1f1b8e6c1b7f4f166e15b7c674945856a51b6/index.html
+++ b/site/recommendations/e2e1f1b8e6c1b7f4f166e15b7c674945856a51b6/index.html
@@ -445,7 +445,7 @@ <h1 id="_1"></h1>
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-12-30 06:05:25 UTC</i>
+  <i class="footer">This page was last updated on 2025-01-06 06:05:43 UTC</i>
   </p>
 
   <div class="note info" onclick="startIntro()">
@@ -544,7 +544,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2024-03-12</td>
           <td>ArXiv</td>
-          <td>82</td>
+          <td>85</td>
           <td>18</td>
         </tr>
 
@@ -568,7 +568,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2024-05-03</td>
           <td>ArXiv</td>
-          <td>13</td>
+          <td>14</td>
           <td>47</td>
         </tr>
 
diff --git a/site/recommendations/e6f0a85009481dcfd93aaa43ed3f980e5033b0d8/index.html b/site/recommendations/e6f0a85009481dcfd93aaa43ed3f980e5033b0d8/index.html
index 902e6cb5..7c1c15a8 100644
--- a/site/recommendations/e6f0a85009481dcfd93aaa43ed3f980e5033b0d8/index.html
+++ b/site/recommendations/e6f0a85009481dcfd93aaa43ed3f980e5033b0d8/index.html
@@ -445,7 +445,7 @@ <h1 id="_1"></h1>
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-12-30 06:05:47 UTC</i>
+  <i class="footer">This page was last updated on 2025-01-06 06:06:11 UTC</i>
   </p>
 
   <div class="note info" onclick="startIntro()">
@@ -496,7 +496,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2015-09-11</td>
           <td>Proceedings of the National Academy of Sciences</td>
-          <td>3476</td>
+          <td>3490</td>
           <td>68</td>
         </tr>
 
@@ -520,7 +520,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2021-11-12</td>
           <td>J. Open Source Softw.</td>
-          <td>124</td>
+          <td>125</td>
           <td>68</td>
         </tr>
 
@@ -544,7 +544,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2020-05-05</td>
           <td>Nature Communications</td>
-          <td>301</td>
+          <td>305</td>
           <td>13</td>
         </tr>
 
@@ -569,7 +569,7 @@ <h3 data-intro='Recommendations for the article'>
           <td>2020-01-31</td>
           <td>IEEE Robotics and Automation Letters</td>
           <td>24</td>
-          <td>24</td>
+          <td>25</td>
         </tr>
 
         <tr id="Many dynamical systems of interest are nonlinear, with examples in turbulence, epidemiology, neuroscience, and finance, making them difficult to control using linear approaches. Model predictive control (MPC) is a powerful model-based optimization technique that enables the control of such nonlinear systems with constraints. However, modern systems often lack computationally tractable models, motivating the use of system identification techniques to learn accurate and efficient models for real-time control. In this tutorial article, we review emerging data-driven methods for model discovery and how they are used for nonlinear MPC. In particular, we focus on the sparse identification of nonlinear dynamics (SINDy) algorithm and show how it may be used with MPC on an infectious disease control example. We compare the performance against MPC based on a linear dynamic mode decomposition (DMD) model. Code is provided to run the tutorial examples and may be modified to extend this data-driven control framework to arbitrary nonlinear systems.">
diff --git a/site/recommendations/f45f85fa1beaa795c24c4ff86f1f2deece72252f/index.html b/site/recommendations/f45f85fa1beaa795c24c4ff86f1f2deece72252f/index.html
index 9f52de2e..645bfac4 100644
--- a/site/recommendations/f45f85fa1beaa795c24c4ff86f1f2deece72252f/index.html
+++ b/site/recommendations/f45f85fa1beaa795c24c4ff86f1f2deece72252f/index.html
@@ -445,7 +445,7 @@ <h1 id="_1"></h1>
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-12-30 06:05:22 UTC</i>
+  <i class="footer">This page was last updated on 2025-01-06 06:05:41 UTC</i>
   </p>
 
   <div class="note info" onclick="startIntro()">
@@ -532,7 +532,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2023-10-03</td>
           <td>ArXiv</td>
-          <td>213</td>
+          <td>214</td>
           <td>9</td>
         </tr>
 
diff --git a/site/recommendations/ff1f1cf9df8c413ec7345da7604ba28597da5b90/index.html b/site/recommendations/ff1f1cf9df8c413ec7345da7604ba28597da5b90/index.html
index b79f81d5..12b2867e 100644
--- a/site/recommendations/ff1f1cf9df8c413ec7345da7604ba28597da5b90/index.html
+++ b/site/recommendations/ff1f1cf9df8c413ec7345da7604ba28597da5b90/index.html
@@ -445,7 +445,7 @@ <h1 id="_1"></h1>
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-12-30 06:05:29 UTC</i>
+  <i class="footer">This page was last updated on 2025-01-06 06:05:46 UTC</i>
   </p>
 
   <div class="note info" onclick="startIntro()">
@@ -483,7 +483,7 @@ <h3 data-intro='Recommendations for the article'>
             Yong Liu, Haoran Zhang, Chenyu Li, Xiangdong Huang, Jianmin Wang, Mingsheng Long
           </td>
           <td>2024-02-04</td>
-          <td>ArXiv, DBLP</td>
+          <td>DBLP, ArXiv</td>
           <td>26</td>
           <td>67</td>
         </tr>
@@ -512,7 +512,7 @@ <h3 data-intro='Recommendations for the article'>
           <td>67</td>
         </tr>
 
-        <tr id="The field of general time series analysis has recently begun to explore unified modeling, where a common architectural backbone can be retrained on a specific task for a specific dataset. In this work, we approach unification from a complementary vantage point: unification across tasks and domains. To this end, we explore the impact of discrete, learnt, time series data representations that enable generalist, cross-domain training. Our method, TOTEM, or TOkenized Time Series EMbeddings, proposes a simple tokenizer architecture that embeds time series data from varying domains using a discrete vectorized representation learned in a self-supervised manner. TOTEM works across multiple tasks and domains with minimal to no tuning. We study the efficacy of TOTEM with an extensive evaluation on 17 real world time series datasets across 3 tasks. We evaluate both the specialist (i.e., training a model on each domain) and generalist (i.e., training a single model on many domains) settings, and show that TOTEM matches or outperforms previous best methods on several popular benchmarks. The code can be found at: https://github.com/SaberaTalukder/TOTEM.">
+        <tr id="This work studies the problem of time series analysis with generalist (or foundation) models, which are models trained across many data domains. Drawing inspiration from the widespread success of large language models, we consider the simple strategy of discretely tokenizing time series data drawn from a myriad of datasets via self-supervision, then using the fixed tokenization to solve a variety of tasks across many data domains. Canonically, time series models are either trained on a single dataset or built in a task-specific manner (e.g., a forecasting-only model), where many use patches of time as inputs to the model. As such, performant generalist, discrete representation time series models explored across many tasks are of value. Our method, TOkenized Time Series EMbeddings (TOTEM), produces such generalist time series models with minimal or no fine-tuning while exhibiting strong zero-shot performance. We evaluate TOTEM extensively over nearly 500 experiments on three commonly-studied time series tasks with real-world data: imputation (17 baselines, 12 datasets), anomaly detection (19 baselines, 25 datasets), and forecasting (14 baselines, 12 datasets). We conclude that TOTEM matches or outperforms existing state-of-the-art models in both the canonical specialist setting (i.e., training one model on one domain) as well as the generalist setting (i.e., training a single model on many domains), which demonstrates the efficacy of tokenization for general time series analysis. The open-source implementation is available here: https://github.com/SaberaTalukder/TOTEM; a video summary is available here: https://www.youtube.com/watch?v=OqrCpdb6MJk.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
           <td><a href="https://www.semanticscholar.org/paper/f9f09c782155ca4f2ae4b6ffcf28514b439226cd" target='_blank'>TOTEM: TOkenized Time Series EMbeddings for General Time Series Analysis</a></td>
           <td>
@@ -532,7 +532,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2024-01-08</td>
           <td>ArXiv</td>
-          <td>6</td>
+          <td>7</td>
           <td>7</td>
         </tr>
 
@@ -544,7 +544,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2024-03-12</td>
           <td>ArXiv</td>
-          <td>82</td>
+          <td>85</td>
           <td>18</td>
         </tr>
 
diff --git a/site/search/search_index.json b/site/search/search_index.json
index aa334e14..809118b6 100644
--- a/site/search/search_index.json
+++ b/site/search/search_index.json
@@ -1 +1 @@
-{"config":{"lang":["en"],"separator":"[\\s\\-]+","pipeline":["stopWordFilter"]},"docs":[{"location":"","title":"Home","text":"Introduction <p>Welcome to Team VPE's Literature Survey System! This project leverages the powerful Semantic Scholar's Recommendation API to provide you with highly relevant research article recommendations based on your curated lists of articles.</p> <p>Moreover, this website contains curated collection of references on differentiable and learned simulator algorithms for developing digital twins with applications in drug discovery and development.</p> Features <ul> <li>List-based recommendations: For each topic, we use a manually curated list of positive articles. We then select an equal number of negative articles from other topics. Semantics Scholar's recommendation system uses the set of positive and negative to provide up to 300 recommendations per topic.</li> <li>Single-paper recommendations: For each article in our curated lists, Semantics Scholar's recommendation system returns up to 10 related articles.</li> </ul> How it works? <ul> <li>Scroll to the top of this page and click one of the tabs to open the relevant section.</li> <li>Each topic contains two tables. The first table lists the manually curated articles, and the second table lists the articles recommended for that topic by the recommendation system. The last column of the first table contains a hyperlink that opens a new tab with articles recommended for that specific article.</li> <li>Click on the help icon at the top of the page to learn more about that section.</li> </ul>         Check out our GitHub open_in_new repository to learn how to build one for yourself."},{"location":"Symbolic%20regression/","title":"Symbolic regression","text":"<p> This page was last updated on 2024-12-30 06:05:56 UTC </p> <p>          Click here for a quick intro of the page! help </p> <p> </p> <p> </p>"},{"location":"Symbolic%20regression/#manually_curated_articles","title":"Manually curated articles on Symbolic regression","text":"Abstract Title Authors Publication Date Journal/ Conference Citation count Highest h-index                View recommendations                visibility_off                  Discovering governing equations from data by sparse identification of nonlinear dynamical systems                               S. Brunton, J. Proctor, J. Kutz            2015-09-11 Proceedings of the National Academy of Sciences, Proceedings of the National Academy of Sciences of the United States of America 3476 68 open_in_new visibility_off                  Robust learning from noisy, incomplete, high-dimensional experimental data via physically constrained symbolic regression                               Patrick A. K. Reinbold, Logan Kageorge, M. Schatz, R. Grigoriev            2021-02-24 Nature Communications 92 24 open_in_new visibility_off                  Data-driven discovery of coordinates and governing equations                               Kathleen P. Champion, Bethany Lusch, J. Kutz, S. Brunton            2019-03-29 Proceedings of the National Academy of Sciences of the United States of America 661 68 open_in_new visibility_off                  Chaos as an intermittently forced linear system                               S. Brunton, Bingni W. Brunton, J. Proctor, E. Kaiser, J. Kutz            2016-08-18 Nature Communications 480 68 open_in_new visibility_off                  Sparse identification of nonlinear dynamics for model predictive control in the low-data limit                               E. Kaiser, J. Kutz, S. Brunton            2017-11-15 Proceedings. Mathematical, Physical, and Engineering Sciences, Proceedings of the Royal Society A 470 68 open_in_new visibility_off                  Inferring Biological Networks by Sparse Identification of Nonlinear Dynamics                               N. Mangan, S. Brunton, J. Proctor, J. Kutz            2016-05-26 IEEE Transactions on Molecular, Biological and Multi-Scale Communications, IEEE Transactions on Molecular Biological and Multi-Scale Communications 339 68 open_in_new visibility_off                  SINDy-PI: a robust algorithm for parallel implicit sparse identification of nonlinear dynamics                               Kadierdan Kaheman, J. Kutz, S. Brunton            2020-04-05 Proceedings. Mathematical, Physical, and Engineering Sciences, Proceedings of the Royal Society A 225 68 open_in_new visibility_off                  Multidimensional Approximation of Nonlinear Dynamical Systems                               Patrick Gel\u00df, Stefan Klus, J. Eisert, Christof Schutte            2018-09-07 Journal of Computational and Nonlinear Dynamics 65 80 open_in_new visibility_off                  Learning Discrepancy Models From Experimental Data                               Kadierdan Kaheman, E. Kaiser, B. Strom, J. Kutz, S. Brunton            2019-09-18 ArXiv, arXiv.org 36 68 open_in_new visibility_off                  Discovery of Physics From Data: Universal Laws and Discrepancies                               Brian M. de Silva, D. Higdon, S. Brunton, J. Kutz            2019-06-19 Frontiers in Artificial Intelligence 78 68 open_in_new visibility_off                  Data-driven discovery of partial differential equations                               S. Rudy, S. Brunton, J. Proctor, J. Kutz            2016-09-21 Science Advances 1252 68 open_in_new visibility_off                  Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control                               Urban Fasel, J. Kutz, Bingni W. Brunton, S. Brunton            2021-11-22 Proceedings. Mathematical, Physical, and Engineering Sciences, Proceedings of the Royal Society A 186 68 open_in_new visibility_off                  Learning sparse nonlinear dynamics via mixed-integer optimization                               D. Bertsimas, Wes Gurnee            2022-06-01 Nonlinear Dynamics 31 93 open_in_new visibility_off                  A Unified Framework for Sparse Relaxed Regularized Regression: SR3                               P. Zheng, T. Askham, S. Brunton, J. Kutz, A. Aravkin            2018-07-14 IEEE Access 125 68 open_in_new Abstract Title Authors Publication Date Journal/ Conference Citation count Highest h-index View recommendations"},{"location":"Symbolic%20regression/#recommended_articles","title":"Recommended articles on Symbolic regression","text":"Abstract Title Authors Publication Date Journal/Conference Citation count Highest h-index visibility_off                LES-SINDy: Laplace-Enhanced Sparse Identification of Nonlinear Dynamical Systems                             Haoyang Zheng, Guang Lin            2024-11-04 ArXiv 0 1 visibility_off                Interpretable and Efficient Data-driven Discovery and Control of Distributed Systems                             Florian Wolf, Nicol\u00f2 Botteghi, Urban Fasel, Andrea Manzoni            2024-11-06 ArXiv 0 11 visibility_off                Compressive\u2010Sensing\u2010Assisted Mixed Integer Optimization for Dynamical System Discovery With Highly Noisy Data                             Tony Shi, Mason Ma, Hoang Tran, Guannan Zhang            2024-12-04 Numerical Methods for Partial Differential Equations 0 1 visibility_off                Automated Global Analysis of Experimental Dynamics through Low-Dimensional Linear Embeddings                             Samuel A. 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Syst. 11 33 Abstract Title Authors Publication Date Journal/Conference Citation count Highest h-index </p>"},{"location":"recommendations/883547fdbd88552328a6615ec620f96e39c57018/","title":"883547fdbd88552328a6615ec620f96e39c57018","text":""},{"location":"recommendations/883547fdbd88552328a6615ec620f96e39c57018/#_1","title":"883547fdbd88552328a6615ec620f96e39c57018","text":"<p> This page was last updated on 2024-12-30 06:05:47 UTC </p> <p>          Click here for a quick intro of the page! help </p> <p>      Recommendations for the article Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control Abstract Title Authors Publication Date Journal/ Conference Citation count Highest h-index visibility_off Sparsifying priors for Bayesian uncertainty quantification in model discovery              Seth M. Hirsh, D. Barajas-Solano, J. 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Mathematical, Physical, and Engineering Sciences 225 68 visibility_off Rapid Bayesian identification of sparse nonlinear dynamics from scarce and noisy data              Lloyd Fung, Urban Fasel, M. Juniper            2024-02-23 ArXiv 1 38 visibility_off Discovering governing equations from data by sparse identification of nonlinear dynamical systems              S. Brunton, J. Proctor, J. Kutz            2015-09-11 Proceedings of the National Academy of Sciences 3476 68 visibility_off Sparse identification of nonlinear dynamics in the presence of library and system uncertainty              Andrew O'Brien            2024-01-23 ArXiv 0 0 $\\dot { \\boldsymbol x} = { \\boldsymbol f} ({ \\boldsymbol x})$ . First, we propose, for use in high-noise settings, an extensive toolkit of critically enabling extensions for the SINDy regression method, to progressively cull functionals from an over-complete library and yield a set of sparse equations that regress to the derivate  $\\dot { \\boldsymbol {x}}$ . This toolkit includes: (regression step) weight timepoints based on estimated noise, use ensembles to estimate coefficients, and regress using FFTs; (culling step) leverage linear dependence of functionals, and restore and protect culled functionals based on Figures of Merit (FoMs). In a novel Assessment step, we define FoMs that compare model predictions to the original time-series (i.e.,  ${ \\boldsymbol x}(t)$  rather than  $\\dot { \\boldsymbol {x}}(t)$ ). These innovations can extract sparse governing equations and coefficients from high-noise time-series data (e.g., 300% added noise). For example, it discovers the correct sparse libraries in the Lorenz system, with median coefficient estimate errors equal to 1%\u22123% (for 50% noise), 6%\u22128% (for 100% noise), and 23%\u221225% (for 300% noise). The enabling modules in the toolkit are combined into a single method, but the individual modules can be tactically applied in other equation discovery methods (SINDy or not) to improve results on high-noise data. Second, we propose a technique, applicable to any model discovery method based on  $\\dot { \\boldsymbol x} = { \\boldsymbol f} ({ \\boldsymbol x})$ , to assess the accuracy of a discovered model in the context of non-unique solutions due to noisy data. Currently, this non-uniqueness can obscure a discovered model\u2019s accuracy and thus a discovery method\u2019s effectiveness. We describe a technique that uses linear dependencies among functionals to transform a discovered model into an equivalent form that is closest to the true model, enabling more accurate assessment of a discovered model\u2019s correctness.\"&gt;           visibility_off A Toolkit for Data-Driven Discovery of Governing Equations in High-Noise Regimes              Charles B. Delahunt, J. Kutz            2021-11-08 IEEE Access 18 33 Abstract Title Authors Publication Date Journal/Conference Citation count Highest h-index </p>"},{"location":"recommendations/b2eb064f432557c59ce99834d7dc7817e4687271/","title":"B2eb064f432557c59ce99834d7dc7817e4687271","text":""},{"location":"recommendations/b2eb064f432557c59ce99834d7dc7817e4687271/#_1","title":"B2eb064f432557c59ce99834d7dc7817e4687271","text":"<p> This page was last updated on 2024-12-30 06:05:42 UTC </p> <p>          Click here for a quick intro of the page! help </p> <p>      Recommendations for the article Sparse identification of nonlinear dynamics for model predictive control in the low-data limit Abstract Title Authors Publication Date Journal/ Conference Citation count Highest h-index visibility_off SINDy with Control: A Tutorial              Urban Fasel, E. Kaiser, J. Kutz, Bingni W. Brunton, S. Brunton            2021-08-30 2021 60th IEEE Conference on Decision and Control (CDC) 56 68 visibility_off SINDy vs Hard Nonlinearities and Hidden Dynamics: a Benchmarking Study              Aurelio Raffa Ugolini, Valentina Breschi, Andrea Manzoni, M. Tanelli            2024-03-01 ArXiv 1 2 visibility_off Discovering Interpretable Dynamics by Sparsity Promotion on Energy and the Lagrangian              H. Chu, M. Hayashibe            2020-01-31 IEEE Robotics and Automation Letters 24 24 visibility_off LeARN: Learnable and Adaptive Representations for Nonlinear Dynamics in System Identification              Arunabh Singh, Joyjit Mukherjee            2024-12-16 ArXiv 0 0 visibility_off SINDy-PI: a robust algorithm for parallel implicit sparse identification of nonlinear dynamics              Kadierdan Kaheman, J. Kutz, S. Brunton            2020-04-05 Proceedings. Mathematical, Physical, and Engineering Sciences 225 68 visibility_off Sparse Identification of Nonlinear Dynamics with Side Information (SINDy-SI)              Gabriel F. Machado, Morgan Jones            2023-10-06 2024 American Control Conference (ACC) 2 1 visibility_off Multi-objective SINDy for parameterized model discovery from single transient trajectory data              Javier A. Lemus, Benjamin Herrmann            2024-05-14 ArXiv 0 0 visibility_off Discovering governing equations from data by sparse identification of nonlinear dynamical systems              S. Brunton, J. Proctor, J. Kutz            2015-09-11 Proceedings of the National Academy of Sciences 3476 68 visibility_off PySINDy: A comprehensive Python package for robust sparse system identification              A. Kaptanoglu, Brian M. de Silva, Urban Fasel, Kadierdan Kaheman, Jared L. Callaham, Charles B. Delahunt, Kathleen P. Champion, Jean-Christophe Loiseau, J. Kutz, S. Brunton            2021-11-12 J. Open Source Softw. 124 68 Abstract Title Authors Publication Date Journal/Conference Citation count Highest h-index </p>"},{"location":"recommendations/c0fc3882a9976f6a9cdc3a724bce184b786503da/","title":"C0fc3882a9976f6a9cdc3a724bce184b786503da","text":""},{"location":"recommendations/c0fc3882a9976f6a9cdc3a724bce184b786503da/#_1","title":"C0fc3882a9976f6a9cdc3a724bce184b786503da","text":"<p> This page was last updated on 2024-12-30 06:05:48 UTC </p> <p>          Click here for a quick intro of the page! help </p> <p>      Recommendations for the article A Unified Framework for Sparse Relaxed Regularized Regression: SR3 Abstract Title Authors Publication Date Journal/ Conference Citation count Highest h-index visibility_off Sparse Relaxed Regularized Regression: SR3              P. Zheng, T. Askham, S. Brunton, J. Kutz, A. Aravkin            2018-07-14 ArXiv 9 68 visibility_off Rank-one Convexification for Sparse Regression              Alper Atamt\u00fcrk, A. G\u00f3mez            2019-01-29 ArXiv 48 36 visibility_off Sparse Recovery via Partial Regularization: Models, Theory and Algorithms              Zhaosong Lu, Xiaorui Li            2015-11-23 ArXiv 37 32 visibility_off Structured Regularizers for High-Dimensional Problems: Statistical and Computational Issues              M. Wainwright            2014-01-03 59 96 visibility_off Compressed Sparse Linear Regression              S. Kasiviswanathan, M. Rudelson            2017-07-25 ArXiv 1 30 visibility_off WARPd: A linearly convergent first-order method for inverse problems with approximate sharpness conditions              Matthew J. Colbrook            2021-10-24 ArXiv 2 17 $\\ell _1$ -norm as the loss function for the residual error and utilizes a generalized nonconvex penalty for sparsity inducing. The $\\ell _1$ -loss is less sensitive to outliers in the measurements than the popular  $\\ell _2$-loss, while the nonconvex penalty has the capability of ameliorating the bias problem of the popular convex LASSO penalty and thus can yield more accurate recovery. To solve this nonconvex and nonsmooth minimization formulation efficiently, we propose a first-order algorithm based on alternating direction method of multipliers. A smoothing strategy on the $\\ell _1$ -loss function has been used in deriving the new algorithm to make it convergent. Further, a sufficient condition for the convergence of the new algorithm has been provided for generalized nonconvex regularization. In comparison with several state-of-the-art algorithms, the new algorithm showed better performance in numerical experiments in recovering sparse signals and compressible images. The new algorithm scales well for large-scale problems, as often encountered in image processing.\"&gt;           visibility_off Efficient and Robust Recovery of Sparse Signal and Image Using Generalized Nonconvex Regularization              Fei Wen, L. Pei, Yuan Yang, Wenxian Yu, Peilin Liu            2017-03-23 IEEE Transactions on Computational Imaging 87 32 visibility_off Regularizers for structured sparsity              C. Micchelli, Jean Morales, M. Pontil            2010-10-04 Advances in Computational Mathematics 80 70 visibility_off Regularizers for structured sparsity              C. Micchelli, Jean Morales, M. Pontil            2010-10-04 Advances in Computational Mathematics 80 70 Abstract Title Authors Publication Date Journal/Conference Citation count Highest h-index </p>"},{"location":"recommendations/c3c94ccc094dcf546e8e31c9a42506302e837524/","title":"C3c94ccc094dcf546e8e31c9a42506302e837524","text":""},{"location":"recommendations/c3c94ccc094dcf546e8e31c9a42506302e837524/#_1","title":"C3c94ccc094dcf546e8e31c9a42506302e837524","text":"<p> This page was last updated on 2024-12-30 06:05:28 UTC </p> <p>          Click here for a quick intro of the page! help </p> <p>      Recommendations for the article AZ-whiteness test: a test for signal uncorrelation on spatio-temporal graphs Abstract Title Authors Publication Date Journal/ Conference Citation count Highest h-index visibility_off AZ-whiteness test: a test for uncorrelated noise on spatio-temporal graphs              Daniele Zambon, C. Alippi            2022-04-23 ArXiv 7 50 visibility_off A Survey on Graph Neural Networks for Time Series: Forecasting, Classification, Imputation, and Anomaly Detection              Ming Jin, Huan Yee Koh, Qingsong Wen, Daniele Zambon, C. Alippi, G. I. Webb, Irwin King, Shirui Pan            2023-07-07 IEEE Transactions on Pattern Analysis and Machine Intelligence 92 50 visibility_off Learning Time-Aware Graph Structures for Spatially Correlated Time Series Forecasting              Minbo Ma, Jilin Hu, Christian S. Jensen, Fei Teng, Peng Han, Zhiqiang Xu, Tian-Jie Li            2023-12-27 2024 IEEE 40th International Conference on Data Engineering (ICDE) 1 14 visibility_off Graph construction on complex spatiotemporal data for enhancing graph neural network-based approaches              Stefan Bloemheuvel, J. Hoogen, Martin Atzmueller            2023-09-25 International Journal of Data Science and Analytics 3 6 visibility_off Time-Varying Signals Recovery Via Graph Neural Networks              Jhon A. Castro-Correa, Jhony H. Giraldo, Anindya Mondal, M. Badiey, T. Bouwmans, Fragkiskos D. Malliaros            2023-02-22 ICASSP 2023 - 2023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) 9 42 visibility_off Graph-Time Convolutional Neural Networks: Architecture and Theoretical Analysis              Mohammad Sabbaqi, E. Isufi            2022-06-30 IEEE Transactions on Pattern Analysis and Machine Intelligence 10 22 visibility_off Multivariate Time Series Forecasting With Dynamic Graph Neural ODEs              Ming Jin, Yu Zheng, Yuanhao Li, Siheng Chen, B. Yang, Shirui Pan            2022-02-17 IEEE Transactions on Knowledge and Data Engineering 78 44 visibility_off Dynamic Graph Learning with Long and Short-Term for Multivariate Time Series Anomaly Detection              Yuyin Tian, Rong Gao, Lingyu Yan, Donghua Liu, Zhiwei Ye            2023-09-07 2023 IEEE 12th International Conference on Intelligent Data Acquisition and Advanced Computing Systems: Technology and Applications (IDAACS) 0 4 Abstract Title Authors Publication Date Journal/Conference Citation count Highest h-index </p>"},{"location":"recommendations/ccea298edb788edf821aef58f0952c3e8debc25a/","title":"Ccea298edb788edf821aef58f0952c3e8debc25a","text":""},{"location":"recommendations/ccea298edb788edf821aef58f0952c3e8debc25a/#_1","title":"Ccea298edb788edf821aef58f0952c3e8debc25a","text":"<p> This page was last updated on 2024-12-30 06:05:19 UTC </p> <p>          Click here for a quick intro of the page! help </p> <p>      Recommendations for the article Graph Deep Learning for Time Series Forecasting Abstract Title Authors Publication Date Journal/ Conference Citation count Highest h-index visibility_off TimeGNN: Temporal Dynamic Graph Learning for Time Series Forecasting              Nancy R. Xu, Chrysoula Kosma, M. Vazirgiannis            2023-07-27 ArXiv 3 55 visibility_off Balanced Graph Structure Learning for Multivariate Time Series Forecasting              Weijun Chen, Yanze Wang, Chengshuo Du, Zhenglong Jia, Feng Liu, Ran Chen            2022-01-24 ArXiv 1 11 visibility_off Sparse Graph Learning from Spatiotemporal Time Series              Andrea Cini, Daniele Zambon, C. Alippi            2022-05-26 J. Mach. Learn. Res. 14 50 visibility_off ForecastGrapher: Redefining Multivariate Time Series Forecasting with Graph Neural Networks              Wanlin Cai, Kun Wang, Hao Wu, Xiaoxu Chen, Yuankai Wu            2024-05-28 ArXiv 0 3 visibility_off Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks              Zonghan Wu, Shirui Pan, Guodong Long, Jing Jiang, Xiaojun Chang, Chengqi Zhang            2020-05-24 Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery &amp; Data Mining 1142 57 visibility_off DeepHGNN: Study of Graph Neural Network based Forecasting Methods for Hierarchically Related Multivariate Time Series              Abishek Sriramulu, Nicolas Fourrier, Christoph Bergmeir            2024-05-29 ArXiv 0 4 visibility_off FourierGNN: Rethinking Multivariate Time Series Forecasting from a Pure Graph Perspective              Kun Yi, Qi Zhang, Wei Fan, Hui He, Liang Hu, Pengyang Wang, Ning An, Longbin Cao, Zhendong Niu            2023-11-10 ArXiv 62 6 Abstract Title Authors Publication Date Journal/Conference Citation count Highest h-index </p>"},{"location":"recommendations/d3dbbd0f0de51b421a6220bd6480b8d2e99a88e9/","title":"D3dbbd0f0de51b421a6220bd6480b8d2e99a88e9","text":""},{"location":"recommendations/d3dbbd0f0de51b421a6220bd6480b8d2e99a88e9/#_1","title":"D3dbbd0f0de51b421a6220bd6480b8d2e99a88e9","text":"<p> This page was last updated on 2024-12-30 06:05:16 UTC </p> <p>          Click here for a quick intro of the page! help </p> <p>      Recommendations for the article A Survey on Graph Neural Networks for Time Series: Forecasting, Classification, Imputation, and Anomaly Detection Abstract Title Authors Publication Date Journal/ Conference Citation count Highest h-index visibility_off Graph Time-series Modeling in Deep Learning: A Survey              Hongjie Chen, Hoda Eldardiry            2023-12-23 ACM Transactions on Knowledge Discovery from Data 5 15 visibility_off A Systematic Literature Review of Spatio-Temporal Graph Neural Network Models for Time Series Forecasting and Classification              Flavio Corradini, Marco Gori, Carlo Lucheroni, Marco Piangerelli, Martina Zannotti            2024-10-29 ArXiv 1 12 visibility_off TimeGNN: Temporal Dynamic Graph Learning for Time Series Forecasting              Nancy R. Xu, Chrysoula Kosma, M. Vazirgiannis            2023-07-27 ArXiv 3 55 visibility_off Graph Deep Learning for Time Series Forecasting              Andrea Cini, Ivan Marisca, Daniele Zambon, C. Alippi            2023-10-24 ArXiv 9 50 visibility_off Graph Anomaly Detection in Time Series: A Survey              Thi Kieu Khanh Ho, Ali Karami, N. Armanfard            2023-01-31 ArXiv 3 15 visibility_off Multivariate Time-Series Anomaly Detection based on Enhancing Graph Attention Networks with Topological Analysis              Zhe Liu, Xiang Huang, Jingyun Zhang, Zhifeng Hao, L. Sun, Hao Peng            2024-08-23 ArXiv, DBLP 0 2 visibility_off FourierGNN: Rethinking Multivariate Time Series Forecasting from a Pure Graph Perspective              Kun Yi, Qi Zhang, Wei Fan, Hui He, Liang Hu, Pengyang Wang, Ning An, Longbin Cao, Zhendong Niu            2023-11-10 ArXiv 62 6 visibility_off MGADN: A Multi-task Graph Anomaly Detection Network for Multivariate Time Series              Wei-Shu Xiong, Xiaochen (Michael) Sun            2022-11-22 ArXiv 1 2 visibility_off Multivariate Time Series Anomaly Detection via Dynamic Graph Forecasting              Katrina Chen, M. Feng, T. Wirjanto            2023-02-04 ArXiv 5 22 visibility_off Edge Conditional Node Update Graph Neural Network for Multi-variate Time Series Anomaly Detection              H. Jo, Seong-Whan Lee            2024-01-25 Inf. Sci. 1 1 Abstract Title Authors Publication Date Journal/Conference Citation count Highest h-index </p>"},{"location":"recommendations/e2a83369383aff37224170c1ae3d3870d5d9e419/","title":"E2a83369383aff37224170c1ae3d3870d5d9e419","text":""},{"location":"recommendations/e2a83369383aff37224170c1ae3d3870d5d9e419/#_1","title":"E2a83369383aff37224170c1ae3d3870d5d9e419","text":"<p> This page was last updated on 2024-12-30 06:05:18 UTC </p> <p>          Click here for a quick intro of the page! help </p> <p>      Recommendations for the article Taming Local Effects in Graph-based Spatiotemporal Forecasting Abstract Title Authors Publication Date Journal/ Conference Citation count Highest h-index visibility_off Graph Deep Learning for Time Series Forecasting              Andrea Cini, Ivan Marisca, Daniele Zambon, C. Alippi            2023-10-24 ArXiv 9 50 visibility_off Scalable Spatiotemporal Graph Neural Networks              Andrea Cini, Ivan Marisca, F. Bianchi, C. Alippi            2022-09-14 ArXiv 37 50 visibility_off Sparse Graph Learning from Spatiotemporal Time Series              Andrea Cini, Daniele Zambon, C. Alippi            2022-05-26 J. Mach. Learn. Res. 14 50 visibility_off Unified Spatio-Temporal Graph Neural Networks: Data-Driven Modeling for Social Science              Yifan Li, Yu Lin, Y. Gao, L. Khan            2022-07-18 2022 International Joint Conference on Neural Networks (IJCNN) 0 12 visibility_off ST-FiT: Inductive Spatial-Temporal Forecasting with Limited Training Data              Zhenyu Lei, Yushun Dong, Jundong Li, Chen Chen            2024-12-14 ArXiv 0 15 visibility_off ForecastGrapher: Redefining Multivariate Time Series Forecasting with Graph Neural Networks              Wanlin Cai, Kun Wang, Hao Wu, Xiaoxu Chen, Yuankai Wu            2024-05-28 ArXiv 0 3 Abstract Title Authors Publication Date Journal/Conference Citation count Highest h-index </p>"},{"location":"recommendations/e2e1f1b8e6c1b7f4f166e15b7c674945856a51b6/","title":"E2e1f1b8e6c1b7f4f166e15b7c674945856a51b6","text":""},{"location":"recommendations/e2e1f1b8e6c1b7f4f166e15b7c674945856a51b6/#_1","title":"E2e1f1b8e6c1b7f4f166e15b7c674945856a51b6","text":"<p> This page was last updated on 2024-12-30 06:05:25 UTC </p> <p>          Click here for a quick intro of the page! help </p> <p>      Recommendations for the article Tiny Time Mixers (TTMs): Fast Pre-trained Models for Enhanced Zero/Few-Shot Forecasting of Multivariate Time Series Abstract Title Authors Publication Date Journal/ Conference Citation count Highest h-index visibility_off VisionTS: Visual Masked Autoencoders Are Free-Lunch Zero-Shot Time Series Forecasters              Mouxiang Chen, Lefei Shen, Zhuo Li, Xiaoyun Joy Wang, Jianling Sun, Chenghao Liu            2024-08-30 ArXiv 0 3 visibility_off A Mamba Foundation Model for Time Series Forecasting              Haoyu Ma, Yushu Chen, Wenlai Zhao, Jinzhe Yang, Yingsheng Ji, Xinghua Xu, Xiaozhu Liu, Hao Jing, Shengzhuo Liu, Guangwen Yang            2024-11-05 ArXiv 0 8 visibility_off Generative Pre-Trained Diffusion Paradigm for Zero-Shot Time Series Forecasting              Jiarui Yang, Tao Dai, Naiqi Li, Junxi Wu, Peiyuan Liu, Jinmin Li, Jigang Bao, Haigang Zhang, Shu-Tao Xia            2024-06-04 ArXiv 1 6 visibility_off Only the Curve Shape Matters: Training Foundation Models for Zero-Shot Multivariate Time Series Forecasting through Next Curve Shape Prediction              Cheng Feng, Long Huang, Denis Krompass            2024-02-12 ArXiv 4 15 visibility_off Lag-Llama: Towards Foundation Models for Probabilistic Time Series Forecasting              Kashif Rasul, Arjun Ashok, Andrew Robert Williams, Arian Khorasani, George Adamopoulos, Rishika Bhagwatkar, Marin Bilovs, Hena Ghonia, N. Hassen, Anderson Schneider, Sahil Garg, Alexandre Drouin, Nicolas Chapados, Yuriy Nevmyvaka, I. Rish            2023-10-12 ArXiv 29 40 visibility_off Chronos: Learning the Language of Time Series              Abdul Fatir Ansari, Lorenzo Stella, Caner Turkmen, Xiyuan Zhang, Pedro Mercado, Huibin Shen, Oleksandr Shchur, Syama Sundar Rangapuram, Sebastian Pineda Arango, Shubham Kapoor, Jasper Zschiegner, Danielle C. Maddix, Michael W. Mahoney, Kari Torkkola, Andrew Gordon Wilson, Michael Bohlke-Schneider, Yuyang Wang            2024-03-12 ArXiv 82 18 visibility_off FoundTS: Comprehensive and Unified Benchmarking of Foundation Models for Time Series Forecasting              Zhe Li, Xiangfei Qiu, Peng Chen, Yihang Wang, Hanyin Cheng, Yang Shu, Jilin Hu, Chenjuan Guo, Aoying Zhou, Qingsong Wen, Christian S. Jensen, Bin Yang            2024-10-15 ArXiv 1 28 visibility_off A Survey of Time Series Foundation Models: Generalizing Time Series Representation with Large Language Model              Jiexia Ye, Weiqi Zhang, Ke Yi, Yongzi Yu, Ziyue Li, Jia Li, F. Tsung            2024-05-03 ArXiv 13 47 Abstract Title Authors Publication Date Journal/Conference Citation count Highest h-index </p>"},{"location":"recommendations/e6f0a85009481dcfd93aaa43ed3f980e5033b0d8/","title":"E6f0a85009481dcfd93aaa43ed3f980e5033b0d8","text":""},{"location":"recommendations/e6f0a85009481dcfd93aaa43ed3f980e5033b0d8/#_1","title":"E6f0a85009481dcfd93aaa43ed3f980e5033b0d8","text":"<p> This page was last updated on 2024-12-30 06:05:47 UTC </p> <p>          Click here for a quick intro of the page! help </p> <p>      Recommendations for the article Learning sparse nonlinear dynamics via mixed-integer optimization Abstract Title Authors Publication Date Journal/ Conference Citation count Highest h-index visibility_off Automatically discovering ordinary differential equations from data with sparse regression              Kevin Egan, Weizhen Li, Rui Carvalho            2024-01-09 Communications Physics 12 2 visibility_off Discovering governing equations from data by sparse identification of nonlinear dynamical systems              S. Brunton, J. Proctor, J. Kutz            2015-09-11 Proceedings of the National Academy of Sciences 3476 68 visibility_off Sparse Identification of Nonlinear Dynamics with Side Information (SINDy-SI)              Gabriel F. Machado, Morgan Jones            2023-10-06 2024 American Control Conference (ACC) 2 1 visibility_off PySINDy: A comprehensive Python package for robust sparse system identification              A. Kaptanoglu, Brian M. de Silva, Urban Fasel, Kadierdan Kaheman, Jared L. Callaham, Charles B. Delahunt, Kathleen P. Champion, Jean-Christophe Loiseau, J. Kutz, S. Brunton            2021-11-12 J. Open Source Softw. 124 68 visibility_off Sparse reconstruction of ordinary differential equations with inference              S. Venkatraman, Sumanta Basu, M. Wells            2023-08-17 ArXiv 0 40 visibility_off Physics-informed learning of governing equations from scarce data              Zhao Chen, Yang Liu, Hao Sun            2020-05-05 Nature Communications 301 13 visibility_off PySINDy: A Python package for the Sparse Identification of Nonlinear Dynamics from Data.              Brian M. de Silva, Kathleen P. Champion, M. Quade, Jean-Christophe Loiseau, J. Kutz, S. Brunton            2020-04-17 arXiv: Dynamical Systems 51 68 visibility_off Discovering Interpretable Dynamics by Sparsity Promotion on Energy and the Lagrangian              H. Chu, M. Hayashibe            2020-01-31 IEEE Robotics and Automation Letters 24 24 visibility_off SINDy with Control: A Tutorial              Urban Fasel, E. Kaiser, J. Kutz, Bingni W. Brunton, S. Brunton            2021-08-30 2021 60th IEEE Conference on Decision and Control (CDC) 56 68 visibility_off Sparse learning of stochastic dynamical equations.              L. Boninsegna, F. N\u00fcske, C. Clementi            2017-12-06 The Journal of chemical physics 202 46 Abstract Title Authors Publication Date Journal/Conference Citation count Highest h-index </p>"},{"location":"recommendations/f45f85fa1beaa795c24c4ff86f1f2deece72252f/","title":"F45f85fa1beaa795c24c4ff86f1f2deece72252f","text":""},{"location":"recommendations/f45f85fa1beaa795c24c4ff86f1f2deece72252f/#_1","title":"F45f85fa1beaa795c24c4ff86f1f2deece72252f","text":"<p> This page was last updated on 2024-12-30 06:05:22 UTC </p> <p>          Click here for a quick intro of the page! help </p> <p>      Recommendations for the article A decoder-only foundation model for time-series forecasting Abstract Title Authors Publication Date Journal/ Conference Citation count Highest h-index visibility_off Lag-Llama: Towards Foundation Models for Probabilistic Time Series Forecasting              Kashif Rasul, Arjun Ashok, Andrew Robert Williams, Arian Khorasani, George Adamopoulos, Rishika Bhagwatkar, Marin Bilovs, Hena Ghonia, N. Hassen, Anderson Schneider, Sahil Garg, Alexandre Drouin, Nicolas Chapados, Yuriy Nevmyvaka, I. Rish            2023-10-12 ArXiv 29 40 visibility_off In-Context Fine-Tuning for Time-Series Foundation Models              Abhimanyu Das, Matthew Faw, Rajat Sen, Yichen Zhou            2024-10-31 ArXiv 0 14 visibility_off Are Language Models Actually Useful for Time Series Forecasting?              Mingtian Tan, Mike A. Merrill, Vinayak Gupta, Tim Althoff, Tom Hartvigsen            2024-06-22 ArXiv 18 3 visibility_off Fine-Tuning a Time Series Foundation Model with Wasserstein Loss              Andrei Chernov            2024-09-18 ArXiv 0 0 visibility_off Time-LLM: Time Series Forecasting by Reprogramming Large Language Models              Ming Jin, Shiyu Wang, Lintao Ma, Zhixuan Chu, James Y. Zhang, X. Shi, Pin-Yu Chen, Yuxuan Liang, Yuan-Fang Li, Shirui Pan, Qingsong Wen            2023-10-03 ArXiv 213 9 visibility_off In-context Time Series Predictor              Jiecheng Lu, Yan Sun, Shihao Yang            2024-05-23 ArXiv 3 2 visibility_off FoundTS: Comprehensive and Unified Benchmarking of Foundation Models for Time Series Forecasting              Zhe Li, Xiangfei Qiu, Peng Chen, Yihang Wang, Hanyin Cheng, Yang Shu, Jilin Hu, Chenjuan Guo, Aoying Zhou, Qingsong Wen, Christian S. Jensen, Bin Yang            2024-10-15 ArXiv 1 28 visibility_off A Mamba Foundation Model for Time Series Forecasting              Haoyu Ma, Yushu Chen, Wenlai Zhao, Jinzhe Yang, Yingsheng Ji, Xinghua Xu, Xiaozhu Liu, Hao Jing, Shengzhuo Liu, Guangwen Yang            2024-11-05 ArXiv 0 8 visibility_off LLM4TS: Aligning Pre-Trained LLMs as Data-Efficient Time-Series Forecasters              Ching Chang, Wenjie Peng, Tien-Fu Chen            2023-08-16 ArXiv 24 3 Abstract Title Authors Publication Date Journal/Conference Citation count Highest h-index </p>"},{"location":"recommendations/ff1f1cf9df8c413ec7345da7604ba28597da5b90/","title":"Ff1f1cf9df8c413ec7345da7604ba28597da5b90","text":""},{"location":"recommendations/ff1f1cf9df8c413ec7345da7604ba28597da5b90/#_1","title":"Ff1f1cf9df8c413ec7345da7604ba28597da5b90","text":"<p> This page was last updated on 2024-12-30 06:05:29 UTC </p> <p>          Click here for a quick intro of the page! help </p> <p>      Recommendations for the article UniTS: A Unified Multi-Task Time Series Model Abstract Title Authors Publication Date Journal/ Conference Citation count Highest h-index visibility_off Timer: Generative Pre-trained Transformers Are Large Time Series Models              Yong Liu, Haoran Zhang, Chenyu Li, Xiangdong Huang, Jianmin Wang, Mingsheng Long            2024-02-04 ArXiv, DBLP 26 67 visibility_off Towards Generalisable Time Series Understanding Across Domains              \u00d6zg\u00fcn Turgut, Philip M\u00fcller, M. Menten, Daniel Rueckert            2024-10-09 ArXiv 0 15 visibility_off Timer-XL: Long-Context Transformers for Unified Time Series Forecasting              Yong Liu, Guo Qin, Xiangdong Huang, Jianmin Wang, Mingsheng Long            2024-10-07 ArXiv 0 67 visibility_off TOTEM: TOkenized Time Series EMbeddings for General Time Series Analysis              Sabera Talukder, Yisong Yue, Georgia Gkioxari            2024-02-26 ArXiv 7 4 visibility_off Universal Time-Series Representation Learning: A Survey              Patara Trirat, Yooju Shin, Junhyeok Kang, Youngeun Nam, Jihye Na, Minyoung Bae, Joeun Kim, Byunghyun Kim, Jae-Gil Lee            2024-01-08 ArXiv 6 7 visibility_off Chronos: Learning the Language of Time Series              Abdul Fatir Ansari, Lorenzo Stella, Caner Turkmen, Xiyuan Zhang, Pedro Mercado, Huibin Shen, Oleksandr Shchur, Syama Sundar Rangapuram, Sebastian Pineda Arango, Shubham Kapoor, Jasper Zschiegner, Danielle C. Maddix, Michael W. Mahoney, Kari Torkkola, Andrew Gordon Wilson, Michael Bohlke-Schneider, Yuyang Wang            2024-03-12 ArXiv 82 18 visibility_off Large Pre-trained time series models for cross-domain Time series analysis tasks              Harshavardhan Kamarthi, B. A. Prakash            2023-11-19 ArXiv 4 9 Abstract Title Authors Publication Date Journal/Conference Citation count Highest h-index </p>"}]}
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+{"config":{"lang":["en"],"separator":"[\\s\\-]+","pipeline":["stopWordFilter"]},"docs":[{"location":"","title":"Home","text":"Introduction <p>Welcome to Team VPE's Literature Survey System! This project leverages the powerful Semantic Scholar's Recommendation API to provide you with highly relevant research article recommendations based on your curated lists of articles.</p> <p>Moreover, this website contains curated collection of references on differentiable and learned simulator algorithms for developing digital twins with applications in drug discovery and development.</p> Features <ul> <li>List-based recommendations: For each topic, we use a manually curated list of positive articles. We then select an equal number of negative articles from other topics. Semantics Scholar's recommendation system uses the set of positive and negative to provide up to 300 recommendations per topic.</li> <li>Single-paper recommendations: For each article in our curated lists, Semantics Scholar's recommendation system returns up to 10 related articles.</li> </ul> How it works? <ul> <li>Scroll to the top of this page and click one of the tabs to open the relevant section.</li> <li>Each topic contains two tables. The first table lists the manually curated articles, and the second table lists the articles recommended for that topic by the recommendation system. The last column of the first table contains a hyperlink that opens a new tab with articles recommended for that specific article.</li> <li>Click on the help icon at the top of the page to learn more about that section.</li> </ul>         Check out our GitHub open_in_new repository to learn how to build one for yourself."},{"location":"Symbolic%20regression/","title":"Symbolic regression","text":"<p> This page was last updated on 2025-01-06 06:06:23 UTC </p> <p>          Click here for a quick intro of the page! help </p> <p> </p> <p> </p>"},{"location":"Symbolic%20regression/#manually_curated_articles","title":"Manually curated articles on Symbolic regression","text":"Abstract Title Authors Publication Date Journal/ Conference Citation count Highest h-index                View recommendations                visibility_off                  Discovering governing equations from data by sparse identification of nonlinear dynamical systems                               S. Brunton, J. Proctor, J. Kutz            2015-09-11 Proceedings of the National Academy of Sciences of the United States of America, Proceedings of the National Academy of Sciences 3490 68 open_in_new visibility_off                  Robust learning from noisy, incomplete, high-dimensional experimental data via physically constrained symbolic regression                               Patrick A. K. Reinbold, Logan Kageorge, M. Schatz, R. Grigoriev            2021-02-24 Nature Communications 93 24 open_in_new visibility_off                  Data-driven discovery of coordinates and governing equations                               Kathleen P. Champion, Bethany Lusch, J. Kutz, S. Brunton            2019-03-29 Proceedings of the National Academy of Sciences of the United States of America 662 68 open_in_new visibility_off                  Chaos as an intermittently forced linear system                               S. Brunton, Bingni W. Brunton, J. Proctor, E. Kaiser, J. Kutz            2016-08-18 Nature Communications 480 68 open_in_new visibility_off                  Sparse identification of nonlinear dynamics for model predictive control in the low-data limit                               E. Kaiser, J. Kutz, S. Brunton            2017-11-15 Proceedings. Mathematical, Physical, and Engineering Sciences, Proceedings of the Royal Society A 472 68 open_in_new visibility_off                  Inferring Biological Networks by Sparse Identification of Nonlinear Dynamics                               N. Mangan, S. Brunton, J. Proctor, J. Kutz            2016-05-26 IEEE Transactions on Molecular Biological and Multi-Scale Communications, IEEE Transactions on Molecular, Biological and Multi-Scale Communications 338 68 open_in_new visibility_off                  SINDy-PI: a robust algorithm for parallel implicit sparse identification of nonlinear dynamics                               Kadierdan Kaheman, J. Kutz, S. Brunton            2020-04-05 Proceedings. Mathematical, Physical, and Engineering Sciences, Proceedings of the Royal Society A 227 68 open_in_new visibility_off                  Multidimensional Approximation of Nonlinear Dynamical Systems                               Patrick Gel\u00df, Stefan Klus, J. Eisert, Christof Schutte            2018-09-07 Journal of Computational and Nonlinear Dynamics 65 80 open_in_new visibility_off                  Learning Discrepancy Models From Experimental Data                               Kadierdan Kaheman, E. Kaiser, B. Strom, J. Kutz, S. Brunton            2019-09-18 arXiv.org, ArXiv 36 68 open_in_new visibility_off                  Discovery of Physics From Data: Universal Laws and Discrepancies                               Brian M. de Silva, D. Higdon, S. Brunton, J. Kutz            2019-06-19 Frontiers in Artificial Intelligence 79 68 open_in_new visibility_off                  Data-driven discovery of partial differential equations                               S. Rudy, S. Brunton, J. Proctor, J. Kutz            2016-09-21 Science Advances 1258 68 open_in_new visibility_off                  Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control                               Urban Fasel, J. Kutz, Bingni W. Brunton, S. Brunton            2021-11-22 Proceedings. Mathematical, Physical, and Engineering Sciences, Proceedings of the Royal Society A 187 68 open_in_new visibility_off                  Learning sparse nonlinear dynamics via mixed-integer optimization                               D. Bertsimas, Wes Gurnee            2022-06-01 Nonlinear Dynamics 32 93 open_in_new visibility_off                  A Unified Framework for Sparse Relaxed Regularized Regression: SR3                               P. Zheng, T. Askham, S. Brunton, J. Kutz, A. Aravkin            2018-07-14 IEEE Access 125 68 open_in_new Abstract Title Authors Publication Date Journal/ Conference Citation count Highest h-index View recommendations"},{"location":"Symbolic%20regression/#recommended_articles","title":"Recommended articles on Symbolic regression","text":"Abstract Title Authors Publication Date Journal/Conference Citation count Highest h-index visibility_off                Learning Weather Models from Data with WSINDy                             Seth Minor, D. Messenger, Vanja Dukic, David M. Bortz            2025-01-01 ArXiv 0 8 visibility_off                Compressive\u2010Sensing\u2010Assisted Mixed Integer Optimization for Dynamical System Discovery With Highly Noisy Data                             Tony Shi, Mason Ma, Hoang Tran, Guannan Zhang            2024-12-04 Numerical Methods for Partial Differential Equations 0 1 visibility_off                Reconstruction of dynamic systems using genetic algorithms with dynamic search limits                             Omar Rodr'iguez-Abreo, Jos'e Luis Arag'on, M. A. Quiroz-Ju'arez            2024-12-03 ArXiv 0 2 visibility_off                Evaluating the Fidelity of Data-Driven Predator-Prey Models: A Dynamical Systems Analysis                             Anna S. Frank, Jiawen Zhang, Sam Subbey            2024-11-15 bioRxiv 0 4 visibility_off                On the relationship between Koopman operator approximations and neural ordinary differential equations for data-driven time-evolution predictions                             Jake Buzhardt, Ricardo Constante-Amores, Michael D. Graham            2024-11-20 ArXiv 0 4 visibility_off                Improved Greedy Identification of Latent Dynamics with Application to Fluid Flows                             R. Ayoub, M. Oulghelou, P. J. Schmid            2024-11-11 ArXiv 0 1 visibility_off                Robust Model-Free Identification of the Causal Networks Underlying Complex Nonlinear Systems                             Guanxue Yang, Shimin Lei, Guanxiao Yang            2024-12-01 Entropy 0 3 visibility_off                Learning Interpretable Network Dynamics via Universal Neural Symbolic Regression                             Jiao Hu, Jiaxu Cui, Bo Yang            2024-11-11 ArXiv 0 5 visibility_off                Universal differential equations for systems biology: Current state and open problems                             Maren Philipps, Nina Schmid, Jan Hasenauer            2024-12-17 bioRxiv 0 0 visibility_off                Modeling Latent Non-Linear Dynamical System over Time Series                             Ren Fujiwara, Yasuko Matsubara, Yasushi Sakurai            2024-12-11 ArXiv 0 13 visibility_off                Data-driven model reconstruction for nonlinear wave dynamics                             E. Smolina, Lev A. Smirnov, Daniel Leykam, Franco Nori, Daria Smirnova            2024-11-18 ArXiv 0 3 visibility_off                LeARN: Learnable and Adaptive Representations for Nonlinear Dynamics in System Identification                             Arunabh Singh, Joyjit Mukherjee            2024-12-16 ArXiv 0 0 visibility_off                Interpretable low-order representation of eigenmode deformation in parameterized dynamical systems                             Nicolas Torres-Ulloa, Erick Kracht, Urban Fasel, Benjamin Herrmann            2024-12-16 ArXiv 0 11 visibility_off                NN-ResDMD: Learning Koopman Representations for Complex Dynamics with Spectral Residuals                             Yuanchao Xu, Kaidi Shao, Nikos Logothetis, Zhongwei Shen            2025-01-01 ArXiv 0 0 visibility_off                A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems                             Xiangnan Yu, Hao Xu, Zhiping Mao, Hongguang Sun, Yong Zhang, Dong-juan Zhang, Yuntian Chen            2024-12-05 ArXiv 0 11 visibility_off                Data-driven optimal control of unknown nonlinear dynamical systems using the Koopman operator                             Zhexuan Zeng, Rui Zhou, Yiming Meng, Jun Liu            2024-12-02 ArXiv 0 9 visibility_off                When are dynamical systems learned from time series data statistically accurate?                             Jeongjin Park, Nicole Yang, N. Chandramoorthy            2024-11-09 ArXiv 1 8 visibility_off                KAN/MultKAN with Physics-Informed Spline fitting (KAN-PISF) for ordinary/partial differential equation discovery of nonlinear dynamic systems                             A. Pal, Satish Nagarajaiah            2024-11-18 ArXiv 0 3 visibility_off                Model order reduction for the cross-diffusive Brusselator Equation                             Tugba K\u00fc\u00e7\u00fckseyhan            2024-11-30 GSC Advanced Research and Reviews 0 5 visibility_off                Unsupervised data-driven response regime exploration and identification for dynamical systems.                             M. Farid            2024-12-01 Chaos 0 8 visibility_off                Learning Koopman-based Stability Certificates for Unknown Nonlinear Systems                             Rui Zhou, Yiming Meng, Zhexuan Zeng, Jun Liu            2024-12-03 ArXiv 0 9 visibility_off                Learning Hidden Physics and System Parameters with Deep Operator Networks                             Vijay Kag, Dibakar Roy Sarkar, Birupaksha Pal, Somdatta Goswami            2024-12-06 ArXiv 0 0 visibility_off                Discovering PDEs Corrections from Data Within a Hybrid Modeling Framework                             C. Ghnatios, F. Chinesta            2024-12-24 Mathematics 0 14 visibility_off                Data-Driven Koopman Based System Identification for Partially Observed Dynamical Systems with Input and Disturbance                             P. Ketthong, Jirayu Samkunta, N. T. Mai, M.A.S. Kamal, I. Murakami, Kou Yamada            2024-12-19 Sci 0 8 visibility_off                Symplectic Neural Flows for Modeling and Discovery                             Priscilla Canizares, Davide Murari, C. Schonlieb, Ferdia Sherry, Zakhar Shumaylov            2024-12-21 ArXiv 0 17 visibility_off                What You See is Not What You Get: Neural Partial Differential Equations and The Illusion of Learning                             Arvind Mohan, A. Chattopadhyay, Jonah Miller            2024-11-22 ArXiv 0 16 visibility_off                DR-PDEE for engineered high-dimensional nonlinear stochastic systems: a physically-driven equation providing theoretical basis for data-driven approaches                             Jian-Bing Chen, , Meng-Ze Lyu            2024-12-06 Nonlinear Dynamics 0 9 visibility_off                Estimating unknown parameters in differential equations with a reinforcement learning based PSO method                             Wenkui Sun, Xiaoya Fan, Lijuan Jia, Tinyi Chu, S. Yau, Rongling Wu, Zhong Wang            2024-11-13 ArXiv 0 112 visibility_off                KH-PINN: Physics-informed neural networks for Kelvin-Helmholtz instability with spatiotemporal and magnitude multiscale                             Jiahao Wu, Yuxin Wu, Xin Li, Guihua Zhang            2024-11-12 ArXiv 0 2 visibility_off                Scientific machine learning in ecological systems: A study on the predator-prey dynamics                             Ranabir Devgupta, R. Dandekar, R. Dandekar, S. Panat            2024-11-11 ArXiv 0 3 visibility_off                Coupled Integral PINN for conservation law                             Yeping Wang, Shihao Yang            2024-11-18 ArXiv 0 0 visibility_off                A System Parametrization for Direct Data-Driven Analysis and Control with Error-in-Variables                             Felix Br\u00e4ndle, Frank Allg\u00f6wer            2024-11-11 ArXiv 0 4 visibility_off                Neural Port-Hamiltonian Differential Algebraic Equations for Compositional Learning of Electrical Networks                             Cyrus Neary, Nathan Tsao, U. Topcu            2024-12-15 ArXiv 0 49 visibility_off                Bifurcation analysis in dynamical systems through integration of machine learning and dynamical systems theory                             Nami Mogharabin, Amin Ghadami            2024-11-27 Journal of Computational and Nonlinear Dynamics 0 2 visibility_off                Forecasting High-dimensional Spatio-Temporal Systems from Sparse Measurements                             Jialin Song, Zezheng Song, Pu Ren, N. Benjamin Erichson, Michael W. Mahoney, Xiaoye Li            2024-11-28 Machine Learning: Science and Technology 0 23 visibility_off                Topological Approach for Data Assimilation                             Max M. Chumley, Firas A. Khasawneh            2024-11-12 ArXiv 0 20 visibility_off                Koopman Based Trajectory Optimization with Mixed Boundaries                             Mohamed Abou-Taleb, Maximilian Raff, Kathrin Flasskamp, C. D. Remy            2024-12-04 ArXiv 0 2 visibility_off                Continual Learning and Lifting of Koopman Dynamics for Linear Control of Legged Robots                             Feihan Li, Abulikemu Abuduweili, Yifan Sun, Rui Chen, Weiye Zhao, Changliu Liu            2024-11-21 ArXiv 1 12 visibility_off                Machine learning prediction of tipping in complex dynamical systems                             Shirin Panahi, Ling-Wei Kong, Mohammadamin Moradi, Zheng-Meng Zhai, Bryan Glaz, Mulugeta Haile, Ying-Cheng Lai            2024-11-25 Physical Review Research 0 10 visibility_off                A polynomial approximation scheme for nonlinear model reduction by moment matching                             Carlos Doebeli, Alessandro Astolfi, D. Kalise, Alessio Moreschini, G. Scarciotti, Joel D. Simard            2024-12-17 ArXiv 0 20 visibility_off                A Survey on Kolmogorov-Arnold Network                             Shriyank Somvanshi, Syed Aaqib Javed, Md Monzurul Islam, Diwas Pandit, Subasish Das            2024-11-09 ArXiv 2 1 visibility_off                Space-time model reduction in the frequency domain                             PeterT. Frame, Aaron Towne            2024-11-20 ArXiv 0 2 visibility_off                SPIKANs: Separable Physics-Informed Kolmogorov-Arnold Networks                             Bruno Jacob, Amanda A. Howard, P. Stinis            2024-11-09 ArXiv 1 14 visibility_off                Picard Iteration for Parameter Estimation in Nonlinear Ordinary Differential Equations                             Aleksandr Talitckii, Matthew M. Peet            2024-12-28 ArXiv 0 4 visibility_off                Model Predictive Control of Nonlinear Dynamics Using Online Adaptive Koopman Operators                             Daisuke Uchida, Karthik Duraisamy            2024-12-04 ArXiv 0 3 visibility_off                GraphGrad: Efficient Estimation of Sparse Polynomial Representations for General State-Space Models                             Benjamin Cox, \u00c9milie Chouzenoux, V\u00edctor Elvira            2024-11-23 ArXiv 0 3 Abstract Title Authors Publication Date Journal/Conference Citation count Highest h-index"},{"location":"Time-series%20forecasting/","title":"Time-series forecasting","text":"<p> This page was last updated on 2025-01-06 06:05:55 UTC </p> <p>          Click here for a quick intro of the page! help </p> <p> </p> <p> </p>"},{"location":"Time-series%20forecasting/#manually_curated_articles","title":"Manually curated articles on Time-series forecasting","text":"Abstract Title Authors Publication Date Journal/ Conference Citation count Highest h-index                View recommendations                visibility_off                  A Survey on Graph Neural Networks for Time Series: Forecasting, Classification, Imputation, and Anomaly Detection                               Ming Jin, Huan Yee Koh, Qingsong Wen, Daniele Zambon, C. Alippi, G. I. Webb, Irwin King, Shirui Pan            2023-07-07 IEEE Transactions on Pattern Analysis and Machine Intelligence 92 50 open_in_new visibility_off                  Graph-Guided Network for Irregularly Sampled Multivariate Time Series                               Xiang Zhang, M. Zeman, Theodoros Tsiligkaridis, M. Zitnik            2021-10-11 International Conference on Learning Representations, ArXiv 93 48 open_in_new visibility_off                  Taming Local Effects in Graph-based Spatiotemporal Forecasting                               Andrea Cini, Ivan Marisca, Daniele Zambon, C. Alippi            2023-02-08 Neural Information Processing Systems, ArXiv 24 50 open_in_new visibility_off                  Sparse Graph Learning from Spatiotemporal Time Series                               Andrea Cini, Daniele Zambon, C. Alippi            2022-05-26 Journal of machine learning research, J. Mach. Learn. Res. 14 50 open_in_new visibility_off                  Graph Deep Learning for Time Series Forecasting                               Andrea Cini, Ivan Marisca, Daniele Zambon, C. Alippi            2023-10-24 arXiv.org, ArXiv 9 50 open_in_new visibility_off                  Large Language Models Are Zero-Shot Time Series Forecasters                               Nate Gruver, Marc Finzi, Shikai Qiu, Andrew Gordon Wilson            2023-10-11 Neural Information Processing Systems, ArXiv 213 14 open_in_new visibility_off                  Graph-Mamba: Towards Long-Range Graph Sequence Modeling with Selective State Spaces                               Chloe X. Wang, Oleksii Tsepa, Jun Ma, Bo Wang            2024-02-01 arXiv.org, ArXiv 62 5 open_in_new visibility_off                  A decoder-only foundation model for time-series forecasting                               Abhimanyu Das, Weihao Kong, Rajat Sen, Yichen Zhou            2023-10-14 International Conference on Machine Learning, ArXiv 120 14 open_in_new visibility_off                  Unified Training of Universal Time Series Forecasting Transformers                               Gerald Woo, Chenghao Liu, Akshat Kumar, Caiming Xiong, Silvio Savarese, Doyen Sahoo            2024-02-04 International Conference on Machine Learning, ArXiv 82 25 open_in_new visibility_off                  Time-LLM: Time Series Forecasting by Reprogramming Large Language Models                               Ming Jin, Shiyu Wang, Lintao Ma, Zhixuan Chu, James Y. Zhang, X. Shi, Pin-Yu Chen, Yuxuan Liang, Yuan-Fang Li, Shirui Pan, Qingsong Wen            2023-10-03 International Conference on Learning Representations, ArXiv 214 9 open_in_new visibility_off                  Tiny Time Mixers (TTMs): Fast Pre-trained Models for Enhanced Zero/Few-Shot Forecasting of Multivariate Time Series                               Vijay Ekambaram, Arindam Jati, Nam H. Nguyen, Pankaj Dayama, Chandra Reddy, Wesley M. Gifford, Jayant Kalagnanam            2024-01-08 arXiv.org, ArXiv 4 4 open_in_new visibility_off                  Self-Supervised Contrastive Pre-Training For Time Series via Time-Frequency Consistency                               Xiang Zhang, Ziyuan Zhao, Theodoros Tsiligkaridis, M. Zitnik            2022-06-17 Neural Information Processing Systems, ArXiv 223 48 open_in_new visibility_off                  Domain Adaptation for Time Series Under Feature and Label Shifts                               Huan He, Owen Queen, Teddy Koker, Consuelo Cuevas, Theodoros Tsiligkaridis, M. Zitnik            2023-02-06 DBLP, ArXiv 43 48 open_in_new visibility_off                  AZ-whiteness test: a test for signal uncorrelation on spatio-temporal graphs                               Daniele Zambon, C. Alippi            None DBLP 6 50 open_in_new visibility_off                  Graph state-space models                               Daniele Zambon, Andrea Cini, L. Livi, C. Alippi            2023-01-04 arXiv.org, ArXiv 4 50 open_in_new visibility_off                  UniTS: A Unified Multi-Task Time Series Model                               Shanghua Gao, Teddy Koker, Owen Queen, Thomas Hartvigsen, Theodoros Tsiligkaridis, M. Zitnik            2024-02-29 ArXiv 4 48 open_in_new Abstract Title Authors Publication Date Journal/ Conference Citation count Highest h-index View recommendations"},{"location":"Time-series%20forecasting/#recommended_articles","title":"Recommended articles on Time-series forecasting","text":"Abstract Title Authors Publication Date Journal/Conference Citation count Highest h-index visibility_off                WaveGNN: Modeling Irregular Multivariate Time Series for Accurate Predictions                             Arash Hajisafi, M. Siampou, Bita Azarijoo, Cyrus Shahabi            2024-12-14 ArXiv 0 3 visibility_off                UTSD: Unified Time Series Diffusion Model                             Xiangkai Ma, Xiaobin Hong, Wenzhong Li, Sanglu Lu            2024-12-04 ArXiv 0 3 visibility_off                Knowledge-enhanced Transformer for Multivariate Long Sequence Time-series Forecasting                             S. T. Kakde, Rony Mitra, Jasashwi Mandal, Manoj Kumar Tiwari            2024-11-17 ArXiv 0 5 visibility_off                In-Depth Review of Neural Network Architectures for Forecasting Heart Rate Time Series Data                             Ekaterina Popovska-Slavova, G. Georgieva-Tsaneva            2024-12-20 Innovative STEM Education 0 7 visibility_off                ChatTime: A Unified Multimodal Time Series Foundation Model Bridging Numerical and Textual Data                             Chengsen Wang, Qi Qi, Jingyu Wang, Haifeng Sun, Zirui Zhuang, Jinming Wu, Lei Zhang, Jianxin Liao            2024-12-16 ArXiv 0 27 visibility_off                A Wave is Worth 100 Words: Investigating Cross-Domain Transferability in Time Series                             Xiangkai Ma, Xiaobin Hong, Wenzhong Li, Sanglu Lu            2024-12-01 ArXiv 0 3 visibility_off                TimeCHEAT: A Channel Harmony Strategy for Irregularly Sampled Multivariate Time Series Analysis                             Jiexi Liu, Meng Cao, Songcan Chen            2024-12-17 ArXiv 0 2 visibility_off                PreMixer: MLP-Based Pre-training Enhanced MLP-Mixers for Large-scale Traffic Forecasting                             Tongtong Zhang, Zhiyong Cui, Bingzhang Wang, Yilong Ren, Haiyang Yu, Pan Deng, Yinhai Wang            2024-12-18 ArXiv 0 3 visibility_off                Ister: Inverted Seasonal-Trend Decomposition Transformer for Explainable Multivariate Time Series Forecasting                             Fanpu Cao, Shu Yang, Zhengjian Chen, Ye Liu, Laizhong Cui            2024-12-25 ArXiv 0 0 visibility_off                MFF-FTNet: Multi-scale Feature Fusion across Frequency and Temporal Domains for Time Series Forecasting                             Yangyang Shi, Qianqian Ren, Yong Liu, Jianguo Sun            2024-11-26 ArXiv 0 0 visibility_off                Zero-Shot Load Forecasting with Large Language Models                             Wenlong Liao, Zhe Yang, Mengshuo Jia, Christian Rehtanz, Jiannong Fang, Fernando Port'e-Agel            2024-11-18 ArXiv 0 6 visibility_off                Generalized Prompt Tuning: Adapting Frozen Univariate Time Series Foundation Models for Multivariate Healthcare Time Series                             Mingzhu Liu, Angela H. Chen, George H. Chen            2024-11-19 ArXiv 0 0 visibility_off                Learning Latent Spaces for Domain Generalization in Time Series Forecasting                             Songgaojun Deng, M. D. Rijke            2024-12-15 ArXiv 0 14 visibility_off                xPatch: Dual-Stream Time Series Forecasting with Exponential Seasonal-Trend Decomposition                             Artyom Stitsyuk, Jaesik Choi            2024-12-23 ArXiv 0 1 visibility_off                DSSRNN: Decomposition-Enhanced State-Space Recurrent Neural Network for Time-Series Analysis                             Ahmad Mohammadshirazi, Ali Nosratifiroozsalari, R. 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