Data-Driven Operator Theoretic Methods for Global Phase Space Learning

TL;DR

This paper introduces a data-driven approach using Koopman operator techniques to analyze the global phase space of nonlinear systems from time-series data, enabling the identification of invariant subsets and stitching local dynamics into a global model.

Contribution

It presents a novel method for constructing a global Koopman operator from local invariant subspace data, facilitating phase space analysis of nonlinear systems.

Findings

Successfully applied to biological and nonlinear systems

Enabled identification of invariant subsets from spectral properties

Allowed stitching local dynamics into a comprehensive global model

Abstract

In this work, we propose to apply the recently developed Koopman operator techniques to explore the global phase space of a nonlinear system from time-series data. In particular, we address the problem of identifying various invariant subsets of a phase space from the spectral properties of the associated Koopman operator constructed from time-series data. Moreover, in the case when the system evolution is known locally in various invariant subspaces, then a phase space stitching result is proposed that can be applied to identify a global Koopman operator. A biological system, bistable toggle switch and a second-order nonlinear system example are considered to illustrate the proposed results. The construction of this global Koopman operator is very helpful in experimental works as multiple experiments can't be run at the same time starting from several initial conditions.