Computing Statistical Moments Via Tensorization of Polynomial Chaos Expansions

We present an algorithm for estimating higher-order statistical moments of multidimensional functions expressed as polynomial chaos expansions (PCE). The algorithm starts by decomposing the PCE into a low-rank tensor network using a combination of tensor-train and Tucker decompositions. It then effi...

ver descrição completa

Detalhes bibliográficos
Autor: Ballester Ripoll, Rafael
Formato: artículo
Fecha de publicación:2024
País:España
Recursos:IE
Repositorio:Repositorio IE
OAI Identifier:oai:repositorio.ie.edu:20.500.14417/4021
Acesso em linha:https://doi.org/10.1137/23M155428X
https://hdl.handle.net/20.500.14417/4021
https://epubs.siam.org/doi/10.1137/23M155428X
Access Level:acceso abierto
Palavra-chave:33 Ciencias Tecnológicas
ODS 9 - Industria, innovación e infraestructura
polynomial chaos expansions
statistical moments
surrogate modeling
tensor decompositions
tensor train decomposition
Tucker decomposition
id ES_bbfc7c9cf776e165d54fa28b7840d3fb
oai_identifier_str oai:repositorio.ie.edu:20.500.14417/4021
network_acronym_str ES
network_name_str España
repository_id_str
spelling Computing Statistical Moments Via Tensorization of Polynomial Chaos ExpansionsBallester Ripoll, Rafael33 Ciencias TecnológicasODS 9 - Industria, innovación e infraestructurapolynomial chaos expansionsstatistical momentssurrogate modelingtensor decompositionstensor train decompositionTucker decompositionWe present an algorithm for estimating higher-order statistical moments of multidimensional functions expressed as polynomial chaos expansions (PCE). The algorithm starts by decomposing the PCE into a low-rank tensor network using a combination of tensor-train and Tucker decompositions. It then efficiently calculates the desired moments in the compressed tensor domain, leveraging the highly linear structure of the network. Using three benchmark engineering functions, we demonstrate that our approach offers substantial speed improvements over alternative algorithms while maintaining a minimal and adjustable approximation error. Additionally, our method can calculate moments even when the input variable distribution is altered, incurring only a small additional computational cost and without requiring retraining of the regressor.YesPublishedSociety for Industrial and Applied Mathematicshttps://ror.org/02jjdwm7520252024info:eu-repo/semantics/articleapplication/pdfapplication/pdfhttps://doi.org/10.1137/23M155428Xhttps://hdl.handle.net/20.500.14417/4021https://epubs.siam.org/doi/10.1137/23M155428Xreponame:Repositorio IEinstname:IEInglésIE School of Science & TechnologyIE UniversityApplied MathematicsAttribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:repositorio.ie.edu:20.500.14417/40212026-06-15T12:40:57Z
dc.title.none.fl_str_mv Computing Statistical Moments Via Tensorization of Polynomial Chaos Expansions
title Computing Statistical Moments Via Tensorization of Polynomial Chaos Expansions
spellingShingle Computing Statistical Moments Via Tensorization of Polynomial Chaos Expansions
Ballester Ripoll, Rafael
33 Ciencias Tecnológicas
ODS 9 - Industria, innovación e infraestructura
polynomial chaos expansions
statistical moments
surrogate modeling
tensor decompositions
tensor train decomposition
Tucker decomposition
title_short Computing Statistical Moments Via Tensorization of Polynomial Chaos Expansions
title_full Computing Statistical Moments Via Tensorization of Polynomial Chaos Expansions
title_fullStr Computing Statistical Moments Via Tensorization of Polynomial Chaos Expansions
title_full_unstemmed Computing Statistical Moments Via Tensorization of Polynomial Chaos Expansions
title_sort Computing Statistical Moments Via Tensorization of Polynomial Chaos Expansions
dc.creator.none.fl_str_mv Ballester Ripoll, Rafael
author Ballester Ripoll, Rafael
author_facet Ballester Ripoll, Rafael
author_role author
dc.contributor.none.fl_str_mv https://ror.org/02jjdwm75
dc.subject.none.fl_str_mv 33 Ciencias Tecnológicas
ODS 9 - Industria, innovación e infraestructura
polynomial chaos expansions
statistical moments
surrogate modeling
tensor decompositions
tensor train decomposition
Tucker decomposition
topic 33 Ciencias Tecnológicas
ODS 9 - Industria, innovación e infraestructura
polynomial chaos expansions
statistical moments
surrogate modeling
tensor decompositions
tensor train decomposition
Tucker decomposition
description We present an algorithm for estimating higher-order statistical moments of multidimensional functions expressed as polynomial chaos expansions (PCE). The algorithm starts by decomposing the PCE into a low-rank tensor network using a combination of tensor-train and Tucker decompositions. It then efficiently calculates the desired moments in the compressed tensor domain, leveraging the highly linear structure of the network. Using three benchmark engineering functions, we demonstrate that our approach offers substantial speed improvements over alternative algorithms while maintaining a minimal and adjustable approximation error. Additionally, our method can calculate moments even when the input variable distribution is altered, incurring only a small additional computational cost and without requiring retraining of the regressor.
publishDate 2024
dc.date.none.fl_str_mv 2024
2025
dc.type.none.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://doi.org/10.1137/23M155428X
https://hdl.handle.net/20.500.14417/4021
https://epubs.siam.org/doi/10.1137/23M155428X
url https://doi.org/10.1137/23M155428X
https://hdl.handle.net/20.500.14417/4021
https://epubs.siam.org/doi/10.1137/23M155428X
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv IE School of Science & Technology
IE University
Applied Mathematics
dc.rights.none.fl_str_mv Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Society for Industrial and Applied Mathematics
publisher.none.fl_str_mv Society for Industrial and Applied Mathematics
dc.source.none.fl_str_mv reponame:Repositorio IE
instname:IE
instname_str IE
reponame_str Repositorio IE
collection Repositorio IE
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869418073946062848
score 15,812429

Registos relacionados