The structure of reconstructed flows in latent spaces

Reconstructing the flow of a dynamical system from experimental data has been a key tool in the study of nonlinear problems. It allows one to discover the equations ruling the dynamics of a system as well as to quantify its complexity. In this work, we study the topology of the flow reconstructed by...

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Detalles Bibliográficos
Autores: Uribarri, Gonzalo, Mindlin, Bernardo Gabriel
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2020
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/146082
Acceso en línea:http://hdl.handle.net/11336/146082
Access Level:acceso abierto
Palabra clave:neural networks
autoencoders
nonlinear dynamics
chaos
https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
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spelling The structure of reconstructed flows in latent spacesUribarri, GonzaloMindlin, Bernardo Gabrielneural networksautoencodersnonlinear dynamicschaoshttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1Reconstructing the flow of a dynamical system from experimental data has been a key tool in the study of nonlinear problems. It allows one to discover the equations ruling the dynamics of a system as well as to quantify its complexity. In this work, we study the topology of the flow reconstructed by autoencoders, a dimensionality reduction method based on deep neural networks that has recently proved to be a very powerful tool for this task. We show that, although in many cases proper embeddings can be obtained with this method, it is not always the case that the topological structure of the flow is preserved.Fil: Uribarri, Gonzalo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; ArgentinaFil: Mindlin, Bernardo Gabriel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; ArgentinaAmerican Institute of Physics2020-09info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/146082Uribarri, Gonzalo; Mindlin, Bernardo Gabriel; The structure of reconstructed flows in latent spaces; American Institute of Physics; Chaos; 30; 9; 9-2020; 1-91054-1500CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1063/5.0013714info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2024-05-08T14:26:51Zoai:ri.conicet.gov.ar:11336/146082instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982024-05-08 14:26:51.633CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv The structure of reconstructed flows in latent spaces
title The structure of reconstructed flows in latent spaces
spellingShingle The structure of reconstructed flows in latent spaces
Uribarri, Gonzalo
neural networks
autoencoders
nonlinear dynamics
chaos
https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
title_short The structure of reconstructed flows in latent spaces
title_full The structure of reconstructed flows in latent spaces
title_fullStr The structure of reconstructed flows in latent spaces
title_full_unstemmed The structure of reconstructed flows in latent spaces
title_sort The structure of reconstructed flows in latent spaces
dc.creator.none.fl_str_mv Uribarri, Gonzalo
Mindlin, Bernardo Gabriel
author Uribarri, Gonzalo
author_facet Uribarri, Gonzalo
Mindlin, Bernardo Gabriel
author_role author
author2 Mindlin, Bernardo Gabriel
author2_role author
dc.subject.none.fl_str_mv neural networks
autoencoders
nonlinear dynamics
chaos
https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
topic neural networks
autoencoders
nonlinear dynamics
chaos
https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
description Reconstructing the flow of a dynamical system from experimental data has been a key tool in the study of nonlinear problems. It allows one to discover the equations ruling the dynamics of a system as well as to quantify its complexity. In this work, we study the topology of the flow reconstructed by autoencoders, a dimensionality reduction method based on deep neural networks that has recently proved to be a very powerful tool for this task. We show that, although in many cases proper embeddings can be obtained with this method, it is not always the case that the topological structure of the flow is preserved.
publishDate 2020
dc.date.none.fl_str_mv 2020-09
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/146082
Uribarri, Gonzalo; Mindlin, Bernardo Gabriel; The structure of reconstructed flows in latent spaces; American Institute of Physics; Chaos; 30; 9; 9-2020; 1-9
1054-1500
CONICET Digital
CONICET
url http://hdl.handle.net/11336/146082
identifier_str_mv Uribarri, Gonzalo; Mindlin, Bernardo Gabriel; The structure of reconstructed flows in latent spaces; American Institute of Physics; Chaos; 30; 9; 9-2020; 1-9
1054-1500
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1063/5.0013714
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv American Institute of Physics
publisher.none.fl_str_mv American Institute of Physics
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 15.812429

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