NysKoop

Kernel estimators for the Koopman operator with the Nystrom approximation.

This repository contains code to go along the following paper: G. Meanti*, A. Chatalic*, V. R. Kostic, P. Novelli, M. Pontil, L. Rosasco, Estimating Koopman operators with sketching to provably learn large scale dynamical systems, Conference on Neural Information Processing Systems, 2023. Implementing all the algorithms and estimators (the Nystrom versions of KRR, PCR and RRR) described in the paper.

Installing

The code depends on falkon and keops for kernel functions and fast kernel-vector products. PyTorch and numpy are also used for their tensor implementations and linear algebra routines.

To install this package, first update pip and setuptools

pip install -U pip setuptools

then run pip install with the --no-build-isolation flag (otherwise pip will create a mess with pytorch versions):

pip install --no-build-isolation git+https://github.com/Giodiro/NystromKoopman.git

API

The API follows scikit-learn conventions. There are 3 main estimators implemented:

• Nystrom KRR
• Nystrom PCR, with an additional randomized version (faster when the number of Nystrom centers is large)
• Nystrom RRR, with an additional randomized version.

In addition to the canonical fit and predict methods, the estimators implement some additional methods:

• eigenfunctions which provides with eigenvalues of the operator, as well as left and right eigenfunctions
• modes for the Koopman modes
• modes_forecast for making predictions with the Koopman modes

GPU Support

A subset of the estimators can run fully on the GPU, if PyTorch and Falkon are installed properly. In particular the RandomizedKoopmanNystromPcr estimator will run wholly on the GPU. Other estimators, like RandomizedKoopmanNystromRrr should run on the GPU for the most part, but may need to synchronize with the CPU for certain steps.

Examples

The notebooks should provide some thorough examples, which were used to run the experiments contained in the paper. In particular, check out the BigProteins.ipynb notebook for an example of using the randomized versions of PCR and RRR to scale to large datasets.

Citation

If you find this work useful, please cite the following paper:

@inproceedings{nyskoop23,
    title = {Estimating {Koopman} operators with sketching to provably learn large scale dynamical systems},
    author = {Giacomo Meanti and Antoine Chatalic and Vladimir R. Kostic and Pietro Novelli and Massimiliano Pontil and Lorenzo Rosasco},
    year = {2023},
    booktitle = {NeurIPS 2023}
}