Non-intrusive low-rank separated approximation of high-dimensional stochastic models

Handle URI:
http://hdl.handle.net/10754/598981
Title:
Non-intrusive low-rank separated approximation of high-dimensional stochastic models
Authors:
Doostan, Alireza; Validi, AbdoulAhad; Iaccarino, Gianluca
Abstract:
This work proposes a sampling-based (non-intrusive) approach within the context of low-. rank separated representations to tackle the issue of curse-of-dimensionality associated with the solution of models, e.g., PDEs/ODEs, with high-dimensional random inputs. Under some conditions discussed in details, the number of random realizations of the solution, required for a successful approximation, grows linearly with respect to the number of random inputs. The construction of the separated representation is achieved via a regularized alternating least-squares regression, together with an error indicator to estimate model parameters. The computational complexity of such a construction is quadratic in the number of random inputs. The performance of the method is investigated through its application to three numerical examples including two ODE problems with high-dimensional random inputs. © 2013 Elsevier B.V.
Citation:
Doostan A, Validi A, Iaccarino G (2013) Non-intrusive low-rank separated approximation of high-dimensional stochastic models. Computer Methods in Applied Mechanics and Engineering 263: 42–55. Available: http://dx.doi.org/10.1016/j.cma.2013.04.003.
Publisher:
Elsevier BV
Journal:
Computer Methods in Applied Mechanics and Engineering
KAUST Grant Number:
AEA 48803
Issue Date:
Aug-2013
DOI:
10.1016/j.cma.2013.04.003
Type:
Article
ISSN:
0045-7825
Sponsors:
The work of AD and AV was partially supported by the Department of Energy under Advanced Scientific Computing Research Early Career Research Award DE-SC0006402, the National Science Foundation grant DMS-1228359, and the Predictive Science Academic Alliance Program (PSAAP) at Stanford University. GI gratefully acknowledges financial support from KAUST under award AEA 48803.
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Full metadata record

DC FieldValue Language
dc.contributor.authorDoostan, Alirezaen
dc.contributor.authorValidi, AbdoulAhaden
dc.contributor.authorIaccarino, Gianlucaen
dc.date.accessioned2016-02-25T13:50:32Zen
dc.date.available2016-02-25T13:50:32Zen
dc.date.issued2013-08en
dc.identifier.citationDoostan A, Validi A, Iaccarino G (2013) Non-intrusive low-rank separated approximation of high-dimensional stochastic models. Computer Methods in Applied Mechanics and Engineering 263: 42–55. Available: http://dx.doi.org/10.1016/j.cma.2013.04.003.en
dc.identifier.issn0045-7825en
dc.identifier.doi10.1016/j.cma.2013.04.003en
dc.identifier.urihttp://hdl.handle.net/10754/598981en
dc.description.abstractThis work proposes a sampling-based (non-intrusive) approach within the context of low-. rank separated representations to tackle the issue of curse-of-dimensionality associated with the solution of models, e.g., PDEs/ODEs, with high-dimensional random inputs. Under some conditions discussed in details, the number of random realizations of the solution, required for a successful approximation, grows linearly with respect to the number of random inputs. The construction of the separated representation is achieved via a regularized alternating least-squares regression, together with an error indicator to estimate model parameters. The computational complexity of such a construction is quadratic in the number of random inputs. The performance of the method is investigated through its application to three numerical examples including two ODE problems with high-dimensional random inputs. © 2013 Elsevier B.V.en
dc.description.sponsorshipThe work of AD and AV was partially supported by the Department of Energy under Advanced Scientific Computing Research Early Career Research Award DE-SC0006402, the National Science Foundation grant DMS-1228359, and the Predictive Science Academic Alliance Program (PSAAP) at Stanford University. GI gratefully acknowledges financial support from KAUST under award AEA 48803.en
dc.publisherElsevier BVen
dc.subjectCurse-of-dimensionalityen
dc.subjectHydrogen oxidationen
dc.subjectLow-rank approximationen
dc.subjectNon-intrusiveen
dc.subjectSeparated representationen
dc.subjectUncertainty quantificationen
dc.titleNon-intrusive low-rank separated approximation of high-dimensional stochastic modelsen
dc.typeArticleen
dc.identifier.journalComputer Methods in Applied Mechanics and Engineeringen
dc.contributor.institutionUniversity of Colorado at Boulder, Boulder, United Statesen
dc.contributor.institutionStanford University, Palo Alto, United Statesen
kaust.grant.numberAEA 48803en
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