SINDy: Sparse Identification of Nonlinear Dynamics

Implementation of the SINDy algorithm for discovering governing equations from data, applied to pendulum dynamics.

Overview

This project implements symbolic regression using SINDy to identify the pendulum equation $\ddot{z} = -\sin(z)$ from simulated data. It includes:

• Basic SINDy: LASSO regression with sklearn and PyTorch implementations
• Thresholding Algorithms: Sequential Thresholding (ST) and Patient Trend-Aware Thresholding (PTAT)
• SINDy-Autoencoder: Learning dynamics from Cartesian coordinates and video data
• Derivative Propagation: Custom neural network layers for time derivative computation

Usage

Open and run sindy.ipynb in Jupyter:

jupyter notebook sindy.ipynb

Execute cells sequentially to:

1. Simulate pendulum dynamics
2. Train SINDy models with different thresholding methods
3. Build and train SINDy-Autoencoders
4. Evaluate learned equations and visualize results