Work

Koopman representations with irregular time intervals

Year: 2025

Type: article

Abstract: Koopman operator theory has been widely applied to data assimilation problems of real systems governed by dynamics, as the theory allows for data-driven construction of modes of dynamical systems. In many modern problems, these modes often must be learned from data with irregular sampling intervals, as opposed to commonly used regularly sampled data. Here, we propose a framework to recover a Koopman eigenfunction–eigenvalue pair for irregularly sampled data. We show that a Koopman eigenpair can be recovered via a natural optimization problem. We provide technical remarks on the anticipated challenges in optimization and suggest a procedure to address them. Simulation studies under different irregular sampling scenarios verify the robustness of the proposed method in learning Koopman eigenfunctions. Compared with extended dynamic mode decomposition on data resampled via interpolation, our method shows improved eigenfunction–recovery accuracy.

Source: Physica D Nonlinear Phenomena

DOI: 10.1016/j.physd.2025.135062

Authors: Younghwan Cho, Richard Sowers

Institutions: University of Illinois Urbana-Champaign, University of Illinois System

Language: English

Topic: Model Reduction and Neural Networks

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,640

Funders: University of Illinois at Urbana-Champaign, Campus Research Board