Deep Learning for Universal Linear Embeddings of Nonlinear Dynamics

This repository implements the approach from the paper: Deep Learning for Universal Linear Embeddings of Nonlinear Dynamics in PyTorch. It replicates the experiments for the Pendulum, Discrete Spectrum, and Fluid Flow on Attractor, and adds additional experiments on the Lorenz System and the Repressilator Model.

Features

• Multiple Experiments:

  • Pendulum
  • Discrete Spectrum
  • Fluid Flow on Attractor
  • Lorenz System
  • Repressilator Model

• Flexible Architectures:

  • Supports multiple architectural variations for the Koopman Autoencoder and Koopman Operator.
  • Choose between MLP or KAN networks for either or both components.

• Koopman Operator Variations:

  1. Koopman operator with a combination of complex conjugate eigenvalues and real values.
  2. Koopman operator with only complex conjugate eigenvalues or real values.
  3. Ensemble of Koopman operators with complex conjugate and real operators.

• Koopman Implementation:

  • Two variations of KAN networks: "Fast KAN" and "Efficient KAN".

• Dataset:

  • Includes generated datasets for the three main experiments.
  • Dataset generator is provided for additional experiments.

Running Experiments

1. Setup

Before running any experiment, create a YAML configuration file that defines the required hyperparameters, including learning rates, architecture options, and experiment-specific parameters.

2. Training

Use train.py to run the training for your experiment. Specify the path to the YAML file with the hyperparameters.

• Logs: During training, logs will display the Koopman loss for both training and validation datasets, along with the prediction loss for the validation dataset.
• Visualization: Training will also visualize the Koopman loss and prediction loss over time.

3. Evaluation

After training, use evaluate.py to evaluate the model on the test dataset. This script will visualize the results for the specified time series of the system being tested.

File Descriptions

• train.py: Script to run the training, specifying the YAML file with hyperparameters and experiment details.
• evaluate.py: Script to evaluate the trained model on the test dataset and visualize the results.
• Data Files: Contains the generated datasets for the experiments and a generator to create custom datasets.