SINDy Autoencoders for Dynamical Systems (PyTorch Implementation)

This project is inspired by Exercise 14.1 from the course textbook and builds upon the work of Champion et al. (GitHub Repository). Our objective is to explore Sparse Identification of Nonlinear Dynamics (SINDy) combined with autoencoders to model complex dynamical systems.

📌 Project Overview

This project focuses on three classic nonlinear dynamical systems:

• The Lorenz system
• A Lotka-Volterra
• The nonlinear pendulum

We aim to gain a deep understanding of how SINDy Autoencoders work and how they can be used to uncover interpretable dynamical models from high-dimensional data. While the original implementation is provided in TensorFlow, we re-implement the approach from scratch using PyTorch to ensure flexibility, transparency, and reproducibility.

🎯 Objectives

• 📖 Learn and document: Consolidate knowledge on SINDy Autoencoders and present it in an accessible, well-organized format.
• 🧠 Autoencoding dynamics: Train autoencoders to reduce the dimensionality of the input data, encoding it into a latent space.
• 🔍 Sparse modeling: Apply SINDy in the latent space to discover the most parsimonious model that describes the system’s dynamics.
• 🔁 Reproduce and extend: Validate results against the original work and experiment with custom modifications.

🛠️ Implementation Details

• Framework: PyTorch
• Key components:
  • Custom autoencoder architectures
  • SINDy integration in the latent space
  • Training and evaluation pipelines for dynamical systems