Koopman Operator Analysis with Deep Learning

This package implements the data-driven extended dynamic mode decomposition (EDMD) with trainable dictionary [1]. This a generalization of the classical EDMD and is most effective for high dimensional or highly nonlinear problems where a priori choice of dictionary functions are difficult. This package implements iterative algorithms to perform Koopman operator analysis, such as computing eigenfunctions, eigenvalues and modes, using a deep neural network based parameterization of the Koopman dictionary functions.

Installation

This project uses python 3.8. Set up the project for development using the following steps:

1. Create a virtual environment

   $virtualenv -p python3.8 ~/.virtualenvs/koopman

2. Activate the environment

   $source ~/.virtualenvs/koopman/bin/activate

3. Install requirements

   $pip install -r requirements.txt

4. Perform editable install for development

   $pip install .

5. Add this virtual environment to Jupyter by typing

   $python -m ipykernel install --user --name=koopman

Generate Documentation

Generate sphinx documentation:

1. Go to docs directory

   $cd docs

2. Run the build

   $sphinx-build -b html source build

3. You can generate documents by

   $make latexpdf

   Otherwise, open docs/build/index.html with any browser to see the html.

Test Basic Modules

1. Go to folder tests

   $cd tests

2. Test
   • Test dictionaries

     $python test_dictionaries.py

   • Test solvers

     $python test_solvers.py

Quickstart

We use Duffing equation and Van der Pol oscillator as examples to show how to use this package.

Look at examples.

Reference

[1] Li, Q., Dietrich, F., Bollt, E. M., & Kevrekidis, I. G. (2017). Extended dynamic mode decomposition with dictionary learning: A data-driven adaptive spectral decomposition of the Koopman operator. Chaos: An Interdisciplinary Journal of Nonlinear Science, 27(10), 103111..

Contributors

• GUO Yue (NUS)
• LI Qianxiao (NUS)