A quantitative analysis of Koopman operator methods for system identification and predictions

Vista sencilla de ítem
dc.contributor.authorZhang, Christophe
dc.contributor.authorZuazua, Enrique
dc.date.accessioned2025-09-12T12:01:54Z
dc.date.available2025-09-12T12:01:54Z
dc.date.issued2022-12-02
dc.date.updated2025-09-12T12:01:54Z
dc.description.abstractWe give convergence and cost estimates for a data-driven system identification method: given an unknown dynamical system, the aim is to recover its vector field and its flow from trajectory data. It is based on the so-called Koopman operator, which uses the well-known link between differential equations and linear transport equations. Data-driven methods recover specific finite-dimensional approximations of the Koopman operator, which can be understood as a transport operator. We focus on such approximations given by classical finite element spaces, which allow us to give estimates on the approximation of the Koopman operator as well as the solutions of the associated linear transport equation. These approximations are thus relevant objects to solve the system identification problem. We then analyze the convergence of a variant of the generator Extended Dynamic Mode Decomposition (gEDMD) algorithm, one of the main algorithms developed to compute approximations of the Koopman operator from data. We find however that, when combining this algorithm with classical finite element spaces, the results are not satisfactory numerically, as the convergence of the data-driven approximation is too slow for the method to benefit from the accuracy of finite element spaces. In particular, for problems in dimension 1 it is less efficient than direct interpolation methods to recover the vector field. We provide some numerical examples to illustrate this last point.en
dc.description.sponsorshipFunding from the Alexander von Humboldt-Professorship program; the work of EZ is partially funded by the European Unions Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 765579-ConFlex, the Grant MTM2017-92996-C2-1-R COS-NET of MINECO (Spain), the Air Force Office of Scientific Research (AFOSR) under Award No. FA9550-18-1-0242 and the Transregio 154 Project “Mathematical Modelling, Simulation and Optimization Using the Example of Gas Networks” of the German DFGen
dc.identifier.citationZhang, C., & Zuazua, E. (2022). A quantitative analysis of Koopman operator methods for system identification and predictions. Comptes Rendus - Mecanique, 351(1 S), 1-31. https://doi.org/10.5802/CRMECA.138
dc.identifier.doi10.5802/CRMECA.138
dc.identifier.eissn1873-7234
dc.identifier.issn1631-0721
dc.identifier.urihttps://hdl.handle.net/20.500.14454/3608
dc.language.isoeng
dc.publisherAcademie des sciences
dc.subject.otherData-driven approximation
dc.subject.otherExtended dynamic mode decomposition
dc.subject.otherFinite element spaces
dc.subject.otherKoopman operator
dc.subject.otherSystem identification
dc.titleA quantitative analysis of Koopman operator methods for system identification and predictions en
dc.typejournal article
dcterms.accessRightsopen access
oaire.citation.endPage31
oaire.citation.issue1 S
oaire.citation.startPage1
oaire.citation.titleComptes Rendus - Mecanique
oaire.citation.volume351
oaire.licenseConditionhttps://creativecommons.org/licenses/by/4.0/
oaire.versionVoR
Archivos
Bloque original
Mostrando 1 - 1 de 1
Miniatura
Nombre:
zhang_quantitative_2022.pdf
Tamaño:
1.02 MB
Formato:
Adobe Portable Document Format
Descargar
Colecciones
Artículos