Final project of the Data-Driven Algorithms course for the Control and Automation Engineering BSc at Universidade Federal de Santa Catarina in 2023, second semester.
Credits to Luke Polson for the numerical solver (Link).
As the analytical complexity of quantum physics topics increases, numerical approaches are increasingly used. Two common tasks for data-driven applications in this field are (I) model identification, in order to identify a model based on data and (II) model complexity reduction, to perform simulations with a lower computational cost.
The objectives of this project are:
- Run the numerical solver for Schröedinger’s Equation, in order to acquire data. Perform the algorithm for 5 different initial conditions, being one of them the particular case of the harmonic oscillator;
- Apply DMD to identify systems modes, enabling a less costly approach for simulation;
- Identify Schröedinger’s PDE using SINDy algorithm.
With DMD, it was possible to reconstruct the original data with a low error (at the order of
With the reconstruction, it was possible to save around 96% storage size of the time series data.
Also, using SINDy algorithm, it was possible to correctly identify the harmonic oscillator PDE.
First, it is necessary to install the libraries in requirements.txt.
The project has 3 main files:
- "generate_data.ipynb", inside of "1_Generate_Data";
- "dmd_project.ipynb", inside of "2_DMD";
- "harmonic_oscillator.ipynb", inside of "3_SINDy";
Running these 3 notebooks in sequence will reproduce the results.