joseph-crowley/learned-koopman

Explore using cVAEs to learn Koopman Operators for predicting nonlinear harmonic oscillator dynamics.

Nonlinear Harmonic Oscillator: Learning Koopman Operators with cVAE 🎉

Welcome to this exciting repository! 🌟 This project aims to uncover the underlying dynamics of nonlinear harmonic oscillators using Conditional Variational Autoencoders (cVAE) to learn Koopman Operators. This topic is a treasure trove for anyone interested in leveraging machine learning for understanding nonlinear dynamical systems.

What's Inside? 📁

The repository is neatly organized with each file serving a specific purpose:

• ./data_generator.py: Generates time-series data for the nonlinear harmonic oscillator, considering multiple initial conditions.

• ./cVAE.py: Houses the cVAE class, the backbone of our machine learning approach to learning the low-rank approximation of the Koopman Operator.

• ./learn.py: Executes the training loop for our cVAE, optimized with hyperparameters through Bayesian Optimization.

• ./test.py: Evaluates the performance of the trained model and visualizes the predicted dynamics.

Diving into the Machine Learning Magic 🌟

The cVAE.py file contains the blueprint of our Conditional Variational Autoencoder, designed to capture the nonlinear dynamics in its latent space. By learning a Koopman Operator, the cVAE transforms complex, nonlinear dynamics into linear dynamics in the latent space, making future state predictions more tractable.

The data generator in data_generator.py employs numerical methods to simulate the nonlinear harmonic oscillator, creating a rich dataset that considers a wide range of initial conditions.

Finally, test.py allows you to see the learned dynamics in action, comparing predicted states with actual states to measure the model's performance.

Getting Started 🏃

To kickstart your journey, clone this repository:

git clone https://github.com/joseph-crowley/learned-koopman.git
cd learned-koopman

Ensure that you have Python 3.x:

python --version

Install the necessary Python packages:

pip install numpy torch matplotlib

Run the training script to train your very own cVAE:

python learn.py

Contributing 🤝

Your contributions can make this project even better! Feel free to raise issues, propose new features, or contribute to the code/documentation through pull requests. Collaboration is the key to scientific discovery!