Work

General regularization scheme in data-driven learning of Koopman operators

Year: 2024

Type: article

Abstract: As is known, the Koopman operator is widely used in the analysis of complex dynamic systems. In this paper, we consider the problem of numerical representation of the Koopman operators on Reproducing Kernel Hilbert spaces. The main idea of the proposed approach is the use of a concept of general regularization scheme to ensure the stability of the constructed approximations. This concept allows us to simultaneously consider several well-known regularization methods, which have been previously employed for approximating the Koopman operators. We also discuss the issue of the regularization parameter choice, that has been understudied so far.

Source: Journal of Applied and Numerical Analysis

DOI: 10.30970/ana.2024.2.77

Authors: Sergiy Pereverzyev, Sergei Solodky

Institutions: Johann Radon Institute for Computational and Applied Mathematics, National Academy of Sciences of Ukraine, Institute of Mathematics, Justus-Liebig-Universität Gießen

Language: English

Topic: Model Reduction and Neural Networks

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: diamond

Funders: Bundesministerium für Klimaschutz, Umwelt, Energie, Mobilität, Innovation und Technologie, European Commission, Österreichische Forschungsförderungsgesellschaft, Bundesministerium für Digitalisierung und Wirtschaftsstandort

Award: G2314803536