PyKoopman: A Python Package for Data-Driven Approximation of the Koopman Operator

TL;DR

PyKoopman is a Python package that enables data-driven approximation of the Koopman operator, allowing linear analysis and control of nonlinear dynamical systems through dynamic mode decomposition techniques.

Contribution

The paper introduces PyKoopman, a comprehensive Python toolkit for Koopman operator approximation, integrating DMD methods with practical tools and examples for system identification.

Findings

Effective data-driven approximation of Koopman operators

Facilitates linear analysis of nonlinear systems

Provides user-friendly tools and code examples

Abstract

PyKoopman is a Python package for the data-driven approximation of the Koopman operator associated with a dynamical system. The Koopman operator is a principled linear embedding of nonlinear dynamics and facilitates the prediction, estimation, and control of strongly nonlinear dynamics using linear systems theory. In particular, PyKoopman provides tools for data-driven system identification for unforced and actuated systems that build on the equation-free dynamic mode decomposition (DMD) and its variants. In this work, we provide a brief description of the mathematical underpinnings of the Koopman operator, an overview and demonstration of the features implemented in PyKoopman (with code examples), practical advice for users, and a list of potential extensions to PyKoopman. Software is available at http://github.com/dynamicslab/pykoopman