Nonintrusive Polynomial Chaos Expansions for Sensitivity Analysis in Stochastic Differential Equations

Handle URI:
http://hdl.handle.net/10754/626240
Title:
Nonintrusive Polynomial Chaos Expansions for Sensitivity Analysis in Stochastic Differential Equations
Authors:
Jimenez, M. Navarro; Le Maître, O. P.; Knio, Omar
Abstract:
A Galerkin polynomial chaos (PC) method was recently proposed to perform variance decomposition and sensitivity analysis in stochastic differential equations (SDEs), driven by Wiener noise and involving uncertain parameters. The present paper extends the PC method to nonintrusive approaches enabling its application to more complex systems hardly amenable to stochastic Galerkin projection methods. We also discuss parallel implementations and the variance decomposition of the derived quantity of interest within the framework of nonintrusive approaches. In particular, a novel hybrid PC-sampling-based strategy is proposed in the case of nonsmooth quantities of interest (QoIs) but smooth SDE solution. Numerical examples are provided that illustrate the decomposition of the variance of QoIs into contributions arising from the uncertain parameters, the inherent stochastic forcing, and joint effects. The simulations are also used to support a brief analysis of the computational complexity of the method, providing insight on the types of problems that would benefit from the present developments.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Citation:
Jimenez MN, Le Maître OP, Knio OM (2017) Nonintrusive Polynomial Chaos Expansions for Sensitivity Analysis in Stochastic Differential Equations. SIAM/ASA Journal on Uncertainty Quantification 5: 378–402. Available: http://dx.doi.org/10.1137/16m1061989.
Publisher:
Society for Industrial & Applied Mathematics (SIAM)
Journal:
SIAM/ASA Journal on Uncertainty Quantification
Issue Date:
18-Apr-2017
DOI:
10.1137/16m1061989
Type:
Article
ISSN:
2166-2525
Sponsors:
This research was supported by the SRI UQ center of the King Abdullah University of Science and Technology.
Additional Links:
http://epubs.siam.org/doi/10.1137/16M1061989
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorJimenez, M. Navarroen
dc.contributor.authorLe Maître, O. P.en
dc.contributor.authorKnio, Omaren
dc.date.accessioned2017-11-29T11:13:56Z-
dc.date.available2017-11-29T11:13:56Z-
dc.date.issued2017-04-18en
dc.identifier.citationJimenez MN, Le Maître OP, Knio OM (2017) Nonintrusive Polynomial Chaos Expansions for Sensitivity Analysis in Stochastic Differential Equations. SIAM/ASA Journal on Uncertainty Quantification 5: 378–402. Available: http://dx.doi.org/10.1137/16m1061989.en
dc.identifier.issn2166-2525en
dc.identifier.doi10.1137/16m1061989en
dc.identifier.urihttp://hdl.handle.net/10754/626240-
dc.description.abstractA Galerkin polynomial chaos (PC) method was recently proposed to perform variance decomposition and sensitivity analysis in stochastic differential equations (SDEs), driven by Wiener noise and involving uncertain parameters. The present paper extends the PC method to nonintrusive approaches enabling its application to more complex systems hardly amenable to stochastic Galerkin projection methods. We also discuss parallel implementations and the variance decomposition of the derived quantity of interest within the framework of nonintrusive approaches. In particular, a novel hybrid PC-sampling-based strategy is proposed in the case of nonsmooth quantities of interest (QoIs) but smooth SDE solution. Numerical examples are provided that illustrate the decomposition of the variance of QoIs into contributions arising from the uncertain parameters, the inherent stochastic forcing, and joint effects. The simulations are also used to support a brief analysis of the computational complexity of the method, providing insight on the types of problems that would benefit from the present developments.en
dc.description.sponsorshipThis research was supported by the SRI UQ center of the King Abdullah University of Science and Technology.en
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.relation.urlhttp://epubs.siam.org/doi/10.1137/16M1061989en
dc.rightsArchived with thanks to SIAM/ASA Journal on Uncertainty Quantificationen
dc.subjectvariance decompositionen
dc.subjectstochastic differential equationen
dc.subjectpolynomial chaosen
dc.titleNonintrusive Polynomial Chaos Expansions for Sensitivity Analysis in Stochastic Differential Equationsen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalSIAM/ASA Journal on Uncertainty Quantificationen
dc.eprint.versionPublisher's Version/PDFen
dc.contributor.institutionLIMSI-CNRS, UPR-3251, Orsay, Franceen
dc.contributor.institutionDepartment of Mechanical Engineering and Materials Science, Duke University, Durham, NC, USAen
kaust.authorJimenez, M. Navarroen
kaust.authorKnio, Omaren
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