Neural ODEs for Phase Space Estimation

This group project investigates the use of Neural Ordinary Differential Equations (Neural ODEs) as a data-driven method to model dynamical systems directly from trajectory data, without requiring knowledge of the underlying governing equations. The study benchmarks Neural ODE performance against Sparse Identification of Nonlinear Dynamics (SINDy), a state-of-the-art symbolic regression technique for discovering governing equations.

📌 Project Highlights

• Learns phase space dynamics purely from observed trajectories.
• Identifies fixed points and analyses their stability using Jacobian eigenvalue analysis.
• Evaluates interpolation and extrapolation performance.
• Tests capabilities on chaotic systems such as the Lorenz attractor.
• Benchmarks Neural ODEs against SINDy for accuracy and runtime.
• Demonstrates qualitative bifurcation behaviour in systems like the Van der Pol oscillator.

📝 Repository Structure

├── presentation/
│ └── final_presentation.pptx # Final Presentation for the Project
├── report/
│ └── final_report.pdf # Final Report for the Project
├── requirements.txt
├── main.ipynb # All code for the Project in 1 Jupyter Notebook
└── README.md

🚀 Getting Started

Installation

1. Clone the repository:

git clone https://github.com/username/neural-odes-dynamics.git
cd neural-odes-dynamics

2. Install dependencies:

pip install -r requirements.txt