Sparse Pseudo Spectral Projection Methods with Directional Adaptation for Uncertainty Quantification

Handle URI:
http://hdl.handle.net/10754/621416
Title:
Sparse Pseudo Spectral Projection Methods with Directional Adaptation for Uncertainty Quantification
Authors:
Winokur, J.; Kim, D.; Bisetti, Fabrizio ( 0000-0001-5162-7805 ) ; Le Maître, O. P.; Knio, Omar
Abstract:
We investigate two methods to build a polynomial approximation of a model output depending on some parameters. The two approaches are based on pseudo-spectral projection (PSP) methods on adaptively constructed sparse grids, and aim at providing a finer control of the resolution along two distinct subsets of model parameters. The control of the error along different subsets of parameters may be needed for instance in the case of a model depending on uncertain parameters and deterministic design variables. We first consider a nested approach where an independent adaptive sparse grid PSP is performed along the first set of directions only, and at each point a sparse grid is constructed adaptively in the second set of directions. We then consider the application of aPSP in the space of all parameters, and introduce directional refinement criteria to provide a tighter control of the projection error along individual dimensions. Specifically, we use a Sobol decomposition of the projection surpluses to tune the sparse grid adaptation. The behavior and performance of the two approaches are compared for a simple two-dimensional test problem and for a shock-tube ignition model involving 22 uncertain parameters and 3 design parameters. The numerical experiments indicate that whereas both methods provide effective means for tuning the quality of the representation along distinct subsets of parameters, PSP in the global parameter space generally requires fewer model evaluations than the nested approach to achieve similar projection error. In addition, the global approach is better suited for generalization to more than two subsets of directions.
KAUST Department:
King Abdullah University of Science and Technology, Thuwal, Saudi Arabia
Citation:
Winokur J, Kim D, Bisetti F, Le Maître OP, Knio OM (2015) Sparse Pseudo Spectral Projection Methods with Directional Adaptation for Uncertainty Quantification. Journal of Scientific Computing 68: 596–623. Available: http://dx.doi.org/10.1007/s10915-015-0153-x.
Publisher:
Springer Nature
Journal:
Journal of Scientific Computing
Issue Date:
19-Dec-2015
DOI:
10.1007/s10915-015-0153-x
Type:
Article
ISSN:
0885-7474; 1573-7691
Sponsors:
This work was supported by the US Department of Energy (DOE), Office of Science, Office of Advanced Scientific Computing Research, under Award Number DE-SC0008789. The authors wish to express their gratitude to Dr. Cosmin Safta for providing a pre-release version of TChem that enables the simulation of adiabatic combustion at constant volume.
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Full metadata record

DC FieldValue Language
dc.contributor.authorWinokur, J.en
dc.contributor.authorKim, D.en
dc.contributor.authorBisetti, Fabrizioen
dc.contributor.authorLe Maître, O. P.en
dc.contributor.authorKnio, Omaren
dc.date.accessioned2016-11-03T08:28:48Z-
dc.date.available2016-11-03T08:28:48Z-
dc.date.issued2015-12-19en
dc.identifier.citationWinokur J, Kim D, Bisetti F, Le Maître OP, Knio OM (2015) Sparse Pseudo Spectral Projection Methods with Directional Adaptation for Uncertainty Quantification. Journal of Scientific Computing 68: 596–623. Available: http://dx.doi.org/10.1007/s10915-015-0153-x.en
dc.identifier.issn0885-7474en
dc.identifier.issn1573-7691en
dc.identifier.doi10.1007/s10915-015-0153-xen
dc.identifier.urihttp://hdl.handle.net/10754/621416-
dc.description.abstractWe investigate two methods to build a polynomial approximation of a model output depending on some parameters. The two approaches are based on pseudo-spectral projection (PSP) methods on adaptively constructed sparse grids, and aim at providing a finer control of the resolution along two distinct subsets of model parameters. The control of the error along different subsets of parameters may be needed for instance in the case of a model depending on uncertain parameters and deterministic design variables. We first consider a nested approach where an independent adaptive sparse grid PSP is performed along the first set of directions only, and at each point a sparse grid is constructed adaptively in the second set of directions. We then consider the application of aPSP in the space of all parameters, and introduce directional refinement criteria to provide a tighter control of the projection error along individual dimensions. Specifically, we use a Sobol decomposition of the projection surpluses to tune the sparse grid adaptation. The behavior and performance of the two approaches are compared for a simple two-dimensional test problem and for a shock-tube ignition model involving 22 uncertain parameters and 3 design parameters. The numerical experiments indicate that whereas both methods provide effective means for tuning the quality of the representation along distinct subsets of parameters, PSP in the global parameter space generally requires fewer model evaluations than the nested approach to achieve similar projection error. In addition, the global approach is better suited for generalization to more than two subsets of directions.en
dc.description.sponsorshipThis work was supported by the US Department of Energy (DOE), Office of Science, Office of Advanced Scientific Computing Research, under Award Number DE-SC0008789. The authors wish to express their gratitude to Dr. Cosmin Safta for providing a pre-release version of TChem that enables the simulation of adiabatic combustion at constant volume.en
dc.publisherSpringer Natureen
dc.subjectAdaptive sparse gridsen
dc.subjectChemical kineticsen
dc.subjectPolynomial chaosen
dc.subjectPseudo-spectral approximationen
dc.subjectUncertainty quantificationen
dc.titleSparse Pseudo Spectral Projection Methods with Directional Adaptation for Uncertainty Quantificationen
dc.typeArticleen
dc.contributor.departmentKing Abdullah University of Science and Technology, Thuwal, Saudi Arabiaen
dc.identifier.journalJournal of Scientific Computingen
dc.contributor.institutionDepartment of Mechanical Engineering and Materials Science, Duke University, Durham, NC, United Statesen
dc.contributor.institutionLIMSI-CNRS (UPR 3251), Orsay, Franceen
kaust.authorKim, D.en
kaust.authorBisetti, Fabrizioen
kaust.authorKnio, Omaren
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