Sparse approximation of multilinear problems with applications to kernel-based methods in UQ

Handle URI:
http://hdl.handle.net/10754/626181
Title:
Sparse approximation of multilinear problems with applications to kernel-based methods in UQ
Authors:
Nobile, Fabio; Tempone, Raul ( 0000-0003-1967-4446 ) ; Wolfers, Sören
Abstract:
We provide a framework for the sparse approximation of multilinear problems and show that several problems in uncertainty quantification fit within this framework. In these problems, the value of a multilinear map has to be approximated using approximations of different accuracy and computational work of the arguments of this map. We propose and analyze a generalized version of Smolyak’s algorithm, which provides sparse approximation formulas with convergence rates that mitigate the curse of dimension that appears in multilinear approximation problems with a large number of arguments. We apply the general framework to response surface approximation and optimization under uncertainty for parametric partial differential equations using kernel-based approximation. The theoretical results are supplemented by numerical experiments.
KAUST Department:
Applied Mathematics and Computational Science Program
Citation:
Nobile F, Tempone R, Wolfers S (2017) Sparse approximation of multilinear problems with applications to kernel-based methods in UQ. Numerische Mathematik. Available: http://dx.doi.org/10.1007/s00211-017-0932-4.
Publisher:
Springer Nature
Journal:
Numerische Mathematik
KAUST Grant Number:
2281
Issue Date:
16-Nov-2017
DOI:
10.1007/s00211-017-0932-4
Type:
Article
ISSN:
0029-599X; 0945-3245
Sponsors:
S. Wolfers and R. Tempone are members of the KAUST Strategic Research Initiative, Center for Uncertainty Quantification in Computational Sciences and Engineering. R. Tempone received support from the KAUST CRG3 Award Ref: 2281. F. Nobile received support from the Center for ADvanced MOdeling Science (CADMOS). We thank Abdul-Lateef Haji-Ali for many helpful discussions.
Additional Links:
http://link.springer.com/article/10.1007/s00211-017-0932-4
Appears in Collections:
Articles; Applied Mathematics and Computational Science Program

Full metadata record

DC FieldValue Language
dc.contributor.authorNobile, Fabioen
dc.contributor.authorTempone, Raulen
dc.contributor.authorWolfers, Sörenen
dc.date.accessioned2017-11-20T12:48:14Z-
dc.date.available2017-11-20T12:48:14Z-
dc.date.issued2017-11-16en
dc.identifier.citationNobile F, Tempone R, Wolfers S (2017) Sparse approximation of multilinear problems with applications to kernel-based methods in UQ. Numerische Mathematik. Available: http://dx.doi.org/10.1007/s00211-017-0932-4.en
dc.identifier.issn0029-599Xen
dc.identifier.issn0945-3245en
dc.identifier.doi10.1007/s00211-017-0932-4en
dc.identifier.urihttp://hdl.handle.net/10754/626181-
dc.description.abstractWe provide a framework for the sparse approximation of multilinear problems and show that several problems in uncertainty quantification fit within this framework. In these problems, the value of a multilinear map has to be approximated using approximations of different accuracy and computational work of the arguments of this map. We propose and analyze a generalized version of Smolyak’s algorithm, which provides sparse approximation formulas with convergence rates that mitigate the curse of dimension that appears in multilinear approximation problems with a large number of arguments. We apply the general framework to response surface approximation and optimization under uncertainty for parametric partial differential equations using kernel-based approximation. The theoretical results are supplemented by numerical experiments.en
dc.description.sponsorshipS. Wolfers and R. Tempone are members of the KAUST Strategic Research Initiative, Center for Uncertainty Quantification in Computational Sciences and Engineering. R. Tempone received support from the KAUST CRG3 Award Ref: 2281. F. Nobile received support from the Center for ADvanced MOdeling Science (CADMOS). We thank Abdul-Lateef Haji-Ali for many helpful discussions.en
dc.publisherSpringer Natureen
dc.relation.urlhttp://link.springer.com/article/10.1007/s00211-017-0932-4en
dc.rightsThe final publication is available at Springer via http://dx.doi.org/10.1007/s00211-017-0932-4en
dc.titleSparse approximation of multilinear problems with applications to kernel-based methods in UQen
dc.typeArticleen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.identifier.journalNumerische Mathematiken
dc.eprint.versionPost-printen
dc.contributor.institutionMATHICSE-CSQI, École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerlanden
kaust.authorTempone, Raulen
kaust.authorWolfers, Sörenen
kaust.grant.number2281en
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