# kooplearn: A Scikit-Learn Compatible Library of Algorithms for Evolution Operator Learning

arXiv: https://arxiv.org/abs/2512.21409 · HTML: https://mlsanity.com/paper/2512.21409/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 37 references that are in the map.
- First posted on arXiv 24 Dec 2025.

## Builds on (most cited first, 19 of 19)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [VAMPnets: Deep learning of molecular kinetics](https://mlsanity.com/paper/1710.06012/) (2017)
- [Learning Dynamical Systems via Koopman Operator Regression in Reproducing Kernel Hilbert Spaces](https://mlsanity.com/paper/2205.14027/) (2022)
- [Sharp Spectral Rates for Koopman Operator Learning](https://mlsanity.com/paper/2302.02004/) (2023)
- [Koopman Kernel Regression](https://mlsanity.com/paper/2305.16215/) (2023)
- [Learning invariant representations of time-homogeneous stochastic dynamical systems](https://mlsanity.com/paper/2307.09912/) (2023)
- [Estimating Koopman operators with sketching to provably learn large scale dynamical systems](https://mlsanity.com/paper/2306.04520/) (2023)
- [PyDMD: A Python package for robust dynamic mode decomposition](https://mlsanity.com/paper/2402.07463/) (2024)
- [Neural Conditional Probability for Uncertainty Quantification](https://mlsanity.com/paper/2407.01171/) (2024)
- [PyKoopman: A Python Package for Data-Driven Approximation of the Koopman Operator](https://mlsanity.com/paper/2306.12962/) (2023)
- [Consistent Long-Term Forecasting of Ergodic Dynamical Systems](https://mlsanity.com/paper/2312.13426/) (2023)
- [KoopmanLab: machine learning for solving complex physics equations](https://mlsanity.com/paper/2301.01104/) (2023)
- [Learning the Infinitesimal Generator of Stochastic Diffusion Processes](https://mlsanity.com/paper/2405.12940/) (2024)
- [Self-Supervised Evolution Operator Learning for High-Dimensional Dynamical Systems](https://mlsanity.com/paper/2505.18671/) (2025)
- [From Biased to Unbiased Dynamics: An Infinitesimal Generator Approach](https://mlsanity.com/paper/2406.09028/) (2024)
- [Koopman-Equivariant Gaussian Processes](https://mlsanity.com/paper/2502.06645/) (2025)
- [DLKoopman: A deep learning software package for Koopman theory](https://mlsanity.com/paper/2211.08992/) (2022)
- [A randomized algorithm to solve reduced rank operator regression](https://mlsanity.com/paper/2312.17348/) (2023)

## Built on by (most cited first, 1 of 1)

- [Dynamic Mode Decomposition along Depth in Vision Transformers](https://mlsanity.com/paper/2605.07556/) (2026)

## Abstract (arXiv)

kooplearn is a machine-learning library that implements linear, kernel, and deep-learning estimators of dynamical operators and their spectral decompositions. kooplearn can model both discrete-time evolution operators (Koopman/Transfer) and continuous-time infinitesimal generators. By learning these operators, users can analyze dynamical systems via spectral methods, derive data-driven reduced-order models, and forecast future states and observables. kooplearn's interface is compliant with the scikit-learn API, facilitating its integration into existing machine learning and data science workflows. Additionally, kooplearn includes curated benchmark datasets to support experimentation, reproducibility, and the fair comparison of learning algorithms. The software is available at https://github.com/Machine-Learning-Dynamical-Systems/kooplearn.