Modularized data-driven approximation of the Koopman operator and generator

TL;DR

This paper introduces a modularized EDMD approach for approximating the Koopman operator in interconnected systems, enabling scalable analysis, transfer learning, and adaptation to topology changes with finite-data error bounds.

Contribution

It presents a novel modularized EDMD scheme that learns subsystem dynamics individually, reducing dimensionality and supporting transfer learning and topology adaptation.

Findings

Effective in interconnected systems with reduced computational complexity

Supports transfer learning across multiple system copies

Demonstrated with numerical examples showing accuracy and adaptability

Abstract

Extended Dynamic Mode Decomposition (EDMD) is a widely-used data-driven approach to learn an approximation of the Koopman operator. Consequently, it provides a powerful tool for data-driven analysis, prediction, and control of nonlinear dynamical (control) systems. In this work, we propose a novel modularized EDMD scheme tailored to interconnected systems. To this end, we utilize the structure of the Koopman generator that allows to learn the dynamics of subsystems individually and thus alleviates the curse of dimensionality by considering observable functions on smaller state spaces. Moreover, our approach canonically enables transfer learning if a system encompasses multiple copies of a model as well as efficient adaption to topology changes without retraining. We provide finite-data bounds on the estimation error using tools from graph theory. The efficacy of the method is illustrated by means of various numerical examples.