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

Abstract

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.

Figures (4)

• Figure 1: Sketch of the action of an evolution operator on a protein folding trajectory. The dynamics of the protein is linearized by means of a nonlinear representation $\varphi$ and consequently evolved by means of the linear map $E$.
• Figure 2: Comparison between kernel DMD (kDMD) and Reduced Rank estimators. The Reduced Rank estimator provides a more accurate approximation of the leading eigenfunctions of the transfer operator for the overdamped Langevin dynamics.
• Figure 3: Fit time of a Kernel model (Gaussian kernel) on a dataset of $5000$ observations from the Lorenz 63 dynamical system. The results are the median of three independent runs on a system equipped with an Intel Core i9-9900X CPU (3.50GHz) and 48GB of RAM memory.
• Figure 4: Samples from the datasets included in kooplearn.