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

2025-12-24

AI Summary

This work addresses the lack of a unified, reproducible framework for learning evolution operators in dynamical systems modeling. We introduce the first open-source library rigorously compliant with the scikit-learn API, enabling consistent estimation of discrete- and continuous-time evolution operators—including Koopman operators, transfer operators, and infinitesimal generators. The library unifies three major paradigms: linear methods (e.g., DMD), kernel-based approaches, and deep neural operators, and includes standardized benchmark datasets. Key contributions are: (1) the first scikit-learn–compatible framework for dynamical systems learning; (2) an integrated interface supporting spectral decomposition, model reduction, and long-term forecasting within a single workflow; and (3) flexible backend support (PyTorch/TensorFlow) and core numerical algorithms (e.g., SVD, eigen-decomposition). Extensive evaluation on fluid dynamics and chaotic systems demonstrates high accuracy, strong generalization, and interpretability. The library is publicly available and has been widely adopted in the community.

Technology Category

• Machine Learning: Evolutionary Learning
• Search and Optimization: Evolutionary Computation
• Multiagent Systems: Multiagent Learning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Web Mining and Content Analysis: Models for Web evolution

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.

Problem

• Implements algorithms for learning dynamical evolution operators
• Models discrete-time and continuous-time dynamical systems operators
• Enables spectral analysis and forecasting of dynamical systems

Innovation

• Implements linear, kernel, and deep-learning dynamical operator estimators
• Models discrete-time and continuous-time evolution operators for analysis
• Provides scikit-learn compatible API for integration into workflows