Machine learning in viscoelastic fluids via energy-based kernel embedding

The ability to measure differences in collected data is of fundamental importance for quantitative science and machine learning, motivating the establishment of metrics grounded in physical principles. In this study, we focus on the development of such metrics for viscoelastic fluid flows governed b...

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Detalles Bibliográficos
Autores: Otto, Samuel E., Oishi, Cassio M. [UNESP], Amaral, Fabio V.G. [UNESP], Brunton, Steven L., Nathan Kutz, J.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2024
País:Brasil
Institución:Universidade Estadual Paulista (UNESP)
Repositorio:Repositório Institucional da UNESP
Idioma:inglés
OAI Identifier:oai:repositorio.unesp.br:11449/296954
Acceso en línea:http://dx.doi.org/10.1016/j.jcp.2024.113371
https://hdl.handle.net/11449/296954
Access Level:acceso abierto
Palabra clave:Energy-based inner product
Kernel method
Machine learning
Principal component analysis
Reproducing kernel Hilbert space
Viscoelastic flow
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spelling Machine learning in viscoelastic fluids via energy-based kernel embeddingEnergy-based inner productKernel methodMachine learningPrincipal component analysisReproducing kernel Hilbert spaceViscoelastic flowThe ability to measure differences in collected data is of fundamental importance for quantitative science and machine learning, motivating the establishment of metrics grounded in physical principles. In this study, we focus on the development of such metrics for viscoelastic fluid flows governed by a large class of linear and nonlinear stress models. To do this, we introduce energy-compatible families of kernel functions corresponding to a given viscoelastic stress model. Each kernel implicitly embeds flowfield snapshots into a Reproducing Kernel Hilbert Space (RKHS) in which distances and angles are computed and whose squared norm equals the total mechanical energy. Additionally, we present a solution to the preimage problem for these kernels, enabling accurate reconstruction of flowfields from their RKHS representations. Through numerical experiments on an unsteady viscoelastic lid-driven cavity flow, we demonstrate the utility of energy-compatible kernels for extracting energetically-dominant coherent structures in viscoelastic flows across a range of Reynolds and Weissenberg numbers. Specifically, the features extracted by Kernel Principal Component Analysis (KPCA) of flowfield snapshots using energy-compatible kernel functions yield reconstructions with superior accuracy in terms of mechanical energy compared to conventional methods such as ordinary Principal Component Analysis (PCA) with naïvely-defined state vectors or KPCA with ad-hoc choices of kernel functions. Our findings underscore the importance of principled choices of metrics in both scientific and machine learning investigations of complex fluid systems.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Army Research OfficeAI Institute in Dynamic Systems University of WashingtonDepartamento de Matemática e Computação Faculdade de Ciências e Tecnologia São Paulo State UniversityDepartment of Mechanical Engineering University of WashingtonDepartment of Applied Mathematics University of WashingtonSibley School of Mechanical and Aerospace Engineering Cornell UniversityDepartamento de Matemática e Computação Faculdade de Ciências e Tecnologia São Paulo State UniversityFAPESP: 2013/07375-0FAPESP: 2021/07034-4FAPESP: 2021/13833-7FAPESP: 2023/06035-2CNPq: 305383/2019-1CNPq: 307228/2023-1Army Research Office: W911NF-19-1-0045University of WashingtonUniversidade Estadual Paulista (UNESP)Cornell University2025-04-29T18:05:09Z2024-11-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1016/j.jcp.2024.113371Journal of Computational Physics, v. 516.1090-27160021-9991https://hdl.handle.net/11449/29695410.1016/j.jcp.2024.1133712-s2.0-85202354934Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengJournal of Computational Physicsinfo:eu-repo/semantics/openAccessOtto, Samuel E.Oishi, Cassio M. [UNESP]Amaral, Fabio V.G. [UNESP]Brunton, Steven L.Nathan Kutz, J.2025-10-22T18:29:26Zoai:repositorio.unesp.br:11449/296954Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestrepositoriounesp@unesp.bropendoar:29462025-10-22T18:29:26Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Machine learning in viscoelastic fluids via energy-based kernel embedding
title Machine learning in viscoelastic fluids via energy-based kernel embedding
spellingShingle Machine learning in viscoelastic fluids via energy-based kernel embedding
Otto, Samuel E.
Energy-based inner product
Kernel method
Machine learning
Principal component analysis
Reproducing kernel Hilbert space
Viscoelastic flow
title_short Machine learning in viscoelastic fluids via energy-based kernel embedding
title_full Machine learning in viscoelastic fluids via energy-based kernel embedding
title_fullStr Machine learning in viscoelastic fluids via energy-based kernel embedding
title_full_unstemmed Machine learning in viscoelastic fluids via energy-based kernel embedding
title_sort Machine learning in viscoelastic fluids via energy-based kernel embedding
dc.creator.none.fl_str_mv Otto, Samuel E.
Oishi, Cassio M. [UNESP]
Amaral, Fabio V.G. [UNESP]
Brunton, Steven L.
Nathan Kutz, J.
author Otto, Samuel E.
author_facet Otto, Samuel E.
Oishi, Cassio M. [UNESP]
Amaral, Fabio V.G. [UNESP]
Brunton, Steven L.
Nathan Kutz, J.
author_role author
author2 Oishi, Cassio M. [UNESP]
Amaral, Fabio V.G. [UNESP]
Brunton, Steven L.
Nathan Kutz, J.
author2_role author
author
author
author
dc.contributor.none.fl_str_mv University of Washington
Universidade Estadual Paulista (UNESP)
Cornell University
dc.subject.por.fl_str_mv Energy-based inner product
Kernel method
Machine learning
Principal component analysis
Reproducing kernel Hilbert space
Viscoelastic flow
topic Energy-based inner product
Kernel method
Machine learning
Principal component analysis
Reproducing kernel Hilbert space
Viscoelastic flow
description The ability to measure differences in collected data is of fundamental importance for quantitative science and machine learning, motivating the establishment of metrics grounded in physical principles. In this study, we focus on the development of such metrics for viscoelastic fluid flows governed by a large class of linear and nonlinear stress models. To do this, we introduce energy-compatible families of kernel functions corresponding to a given viscoelastic stress model. Each kernel implicitly embeds flowfield snapshots into a Reproducing Kernel Hilbert Space (RKHS) in which distances and angles are computed and whose squared norm equals the total mechanical energy. Additionally, we present a solution to the preimage problem for these kernels, enabling accurate reconstruction of flowfields from their RKHS representations. Through numerical experiments on an unsteady viscoelastic lid-driven cavity flow, we demonstrate the utility of energy-compatible kernels for extracting energetically-dominant coherent structures in viscoelastic flows across a range of Reynolds and Weissenberg numbers. Specifically, the features extracted by Kernel Principal Component Analysis (KPCA) of flowfield snapshots using energy-compatible kernel functions yield reconstructions with superior accuracy in terms of mechanical energy compared to conventional methods such as ordinary Principal Component Analysis (PCA) with naïvely-defined state vectors or KPCA with ad-hoc choices of kernel functions. Our findings underscore the importance of principled choices of metrics in both scientific and machine learning investigations of complex fluid systems.
publishDate 2024
dc.date.none.fl_str_mv 2024-11-01
2025-04-29T18:05:09Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://dx.doi.org/10.1016/j.jcp.2024.113371
Journal of Computational Physics, v. 516.
1090-2716
0021-9991
https://hdl.handle.net/11449/296954
10.1016/j.jcp.2024.113371
2-s2.0-85202354934
url http://dx.doi.org/10.1016/j.jcp.2024.113371
https://hdl.handle.net/11449/296954
identifier_str_mv Journal of Computational Physics, v. 516.
1090-2716
0021-9991
10.1016/j.jcp.2024.113371
2-s2.0-85202354934
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Journal of Computational Physics
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.source.none.fl_str_mv Scopus
reponame:Repositório Institucional da UNESP
instname:Universidade Estadual Paulista (UNESP)
instacron:UNESP
instname_str Universidade Estadual Paulista (UNESP)
instacron_str UNESP
institution UNESP
reponame_str Repositório Institucional da UNESP
collection Repositório Institucional da UNESP
repository.name.fl_str_mv Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)
repository.mail.fl_str_mv repositoriounesp@unesp.br
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score 15,301603

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