General regularization scheme in data-driven learning of Koopman operators
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.
Authors
- S. G. Solodky (ORCID: https://orcid.org/0000-0001-7599-2233)
- Sergiy Pereverzyev (ORCID: https://orcid.org/0000-0002-8627-3995)
Institutions
- National Academy of Sciences of Ukraine (UA)
- Institute of Mathematics (UA)
- Justus-Liebig-Universität Gießen (DE)
- Giessen School of Theology (DE)
- Johann Radon Institute for Computational and Applied Mathematics (AT)
Publication Details
- Journal
- Journal of Applied and Numerical Analysis
- Published
- 2024-12-16
- DOI
- https://doi.org/10.30970/ana.2024.2.77
- Primary Topic
- Numerical methods in inverse problems
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Bundesministerium für Klimaschutz, Umwelt, Energie, Mobilität, Innovation und Technologie
- European Commission
- Österreichische Forschungsförderungsgesellschaft
- Bundesministerium für Digitalisierung und Wirtschaftsstandort