InVAErt networks: a data-driven framework for model synthesis and identifiability analysis

InVAErt networks are designed to perform emulation, inference, and identifiability analysis of physics-based parametric systems.

For additional information, please refer to the publication below:

InVAErt networks: A data-driven framework for model synthesis and identifiability analysis, Guoxiang Grayson Tong, Carlos A. Sing-Long Collao, and Daniele E. Schiavazzi.

Description of the Tools folder

1. DNN_tools.py: common functions for deep neural network modeling
2. Data_generation.py: functions for generating synthetic dataset of each numerical example
3. Model.py: neural network modules
4. NF_tools.py: Specific functions used by the Real-NVP based normalizing flow model
5. Training_tools.py: training and testing functions of the inVAErt networks
6. plotter.py: common and specific plotter functions

Current Jupyter notebooks:

1. Underdetermined_Linear_System.ipynb: Section 4.1 of the paper. Study of an underdetermined linear system with non-trivial null space.
2. Single_sine_wave.ipynb: Section 4.2 of the paper. Study of a simple nonlinear system: sine waves without periodicity.
3. Sine_Waves.ipynb: Section 4.2 of the paper. Study of the former sine waves problem with periodicity.
4. RCR.ipynb: Section 4.3 of the paper. Study of the non-identifiable three-element (R-C-R) Windkessel model.
5. Lotka-Volterra.ipynb: Additional example, not in the paper. Study of the predator-prey model.

Please stay tuned for more Jupyter Notebook tutorials!

Note: the Jupyter notebooks are created for illustration purposes thus the hyper-parameters are adjusted for swift and efficient execution. For more accurate results, we recommend running the code locally with fine-tuned hyper-parameters. Suggested hyper-parameters can be found in the appendix of the paper.

Citation

Did you find this useful? Please cite us using:

@article{tong2024invaert,
  title={InVAErt networks: A data-driven framework for model synthesis and identifiability analysis},
  author={Tong, Guoxiang Grayson and Long, Carlos A Sing and Schiavazzi, Daniele E},
  journal={Computer Methods in Applied Mechanics and Engineering},
  volume={423},
  pages={116846},
  year={2024},
  publisher={Elsevier}
}

Recommended dependencies:

• Pytorch: 2.4.1
• CUDA: 11.8
• Python: 3.10.12
• numpy: 1.26.4
• scipy: 1.12.0
• matplotlib: 3.9.2
• mpi4py: 4.0.0