Kooplearn

kooplearn is a Python library to learn evolution operators — also known as Koopman [1] or Transfer [2] operators — from data. kooplearn models can

1. Predict the evolution of states and observables.

2. Estimate the eigenvalues and eigenfucntions of the learned evolution operators.

3. Compute the dynamic mode decomposition of states and observables.

4. Learn neural-network representations \(x_t \mapsto \varphi(x_t)\) for evolution operators.

Why Choosing kooplearn?

It is easy to use, and strictly adheres to the scikit-learn API. Its Kernel estimators are state-of-the-art, and blazingly fast ⚡️:

Fit time of a Kernel model (Gaussian kernel) on a dataset of 5000 observations from the Lorenz 63 dynamical system. Runned on a system equipped with an Intel Core i9-9900X CPU (3.50GHz) and 48GB of RAM memory.

Fit time of a Kernel model (Gaussian kernel) on a dataset of 5000 observations from the Lorenz 63 dynamical system. Runned on a system equipped with an Intel Core i9-9900X CPU (3.50GHz) and 48GB of RAM memory.

Kooplearn also includes representation learning losses (implemented both in PyTorch and JAX) to train neural-network Koopman embeddings, and offers a collection of datasets for benchmarking evolution operator learning algorithms.

Installation

To install the core version of kooplearn, run

pip

pip install kooplearn

uv

uv add kooplearn

To be able to learn neural-network representations using the representation-learning losses in kooplearn.torch or kooplearn.jax, run

pip

# Torch
pip install "kooplearn[torch]"
# JAX
pip install "kooplearn[jax]"

uv

# Torch
uv add "kooplearn[torch]"
# JAX
uv add "kooplearn[jax]"

Quickstart

import numpy as np
from kooplearn.datasets import make_duffing
from kooplearn.kernel import KernelRidge

# Sample data from the Duffing oscillator
data = make_duffing(X0 = np.array([0, 0]), n_steps=1000)

# Fit the model
model = KernelRidge(n_components=4, kernel='rbf', alpha=1e-5)
model.fit(data)

Citing kooplearn

@article{kooplearn,
  title={kooplearn: A Scikit-Learn Compatible Library of Algorithms for Evolution Operator Learning},
  author={Giacomo Turri and Grégoire Pacreau and Giacomo Meanti and Timothée Devergne and Daniel Ordonez and Erfan Mirzaei and Bruno Belucci and Karim Lounici and Vladimir R. Kostic and Massimiliano Pontil and Pietro Novelli},
  year={2026},
  eprint={2512.21409},
  archivePrefix={arXiv},
  primaryClass={cs.LG},
  url={https://arxiv.org/abs/2512.21409},
}

Learn more

Getting started

examples/linear_system.html

Theory Primer

primer.html

Examples

examples.html

API reference

api/index.html

---

[1]

Bernard O Koopman. Hamiltonian systems and transformation in hilbert space. Proceedings of the National Academy of Sciences, 17(5):315–318, 1931.

[2]

David Applebaum. Lévy Processes and Stochastic Calculus. Cambridge University Press, April 2009. ISBN 9780511809781. URL: http://dx.doi.org/10.1017/CBO9780511809781, doi:10.1017/cbo9780511809781.