Learning Koopman operators for coupled systems via information on governing equations of subsystems

TL;DR

This paper introduces a new method to learn Koopman operators for coupled systems by leveraging the governing differential equations of subsystems, improving stability and accuracy over purely data-driven approaches.

Contribution

The paper presents a novel approach that incorporates subsystem equations to enhance Koopman operator learning for coupled nonlinear systems.

Findings

Method improves stability over EDMD in limited data scenarios.

Numerical experiments show accurate modeling of coupled oscillators.

Approach effectively captures complex interactions in coupled systems.

Abstract

Nonlinear coupled systems are ubiquitous in science and engineering. The analysis and modeling of such systems is challenging due to their high dimensionality and complex interactions among subsystems. In recent years, operator-theoretic methods based on the Koopman operator have attracted attention as a powerful tool for analyzing and modeling nonlinear dynamical systems. Extended dynamic mode decomposition (EDMD) is one of the most popular methods to approximate the Koopman operator. However, EDMD is a purely data-driven method, and it could be unstable and inaccurate for coupled systems under limited data availability. In this paper, we propose a method to learn the Koopman operator for coupled systems using the differential equations governing each subsystem. We also demonstrate its effectiveness through numerical experiments on coupled oscillator systems.