Sampling and Low-Rank Tensor Approximation of the Response Surface

Handle URI:
http://hdl.handle.net/10754/564667
Title:
Sampling and Low-Rank Tensor Approximation of the Response Surface
Authors:
Litvinenko, Alexander ( 0000-0001-5427-3598 ) ; Matthies, Hermann Georg; El-Moselhy, Tarek A.
Abstract:
Most (quasi)-Monte Carlo procedures can be seen as computing some integral over an often high-dimensional domain. If the integrand is expensive to evaluate-we are thinking of a stochastic PDE (SPDE) where the coefficients are random fields and the integrand is some functional of the PDE-solution-there is the desire to keep all the samples for possible later computations of similar integrals. This obviously means a lot of data. To keep the storage demands low, and to allow evaluation of the integrand at points which were not sampled, we construct a low-rank tensor approximation of the integrand over the whole integration domain. This can also be viewed as a representation in some problem-dependent basis which allows a sparse representation. What one obtains is sometimes called a "surrogate" or "proxy" model, or a "response surface". This representation is built step by step or sample by sample, and can already be used for each new sample. In case we are sampling a solution of an SPDE, this allows us to reduce the number of necessary samples, namely in case the solution is already well-represented by the low-rank tensor approximation. This can be easily checked by evaluating the residuum of the PDE with the approximate solution. The procedure will be demonstrated in the computation of a compressible transonic Reynolds-averaged Navier-Strokes flow around an airfoil with random/uncertain data. © Springer-Verlag Berlin Heidelberg 2013.
KAUST Department:
Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Publisher:
Springer Science + Business Media
Journal:
Springer Proceedings in Mathematics & Statistics
Conference/Event name:
10th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, MCQMC 2012
Issue Date:
2013
DOI:
10.1007/978-3-642-41095-6_27
Type:
Conference Paper
ISSN:
21941009
ISBN:
9783642410949
Appears in Collections:
Conference Papers; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorLitvinenko, Alexanderen
dc.contributor.authorMatthies, Hermann Georgen
dc.contributor.authorEl-Moselhy, Tarek A.en
dc.date.accessioned2015-08-04T07:11:36Zen
dc.date.available2015-08-04T07:11:36Zen
dc.date.issued2013en
dc.identifier.isbn9783642410949en
dc.identifier.issn21941009en
dc.identifier.doi10.1007/978-3-642-41095-6_27en
dc.identifier.urihttp://hdl.handle.net/10754/564667en
dc.description.abstractMost (quasi)-Monte Carlo procedures can be seen as computing some integral over an often high-dimensional domain. If the integrand is expensive to evaluate-we are thinking of a stochastic PDE (SPDE) where the coefficients are random fields and the integrand is some functional of the PDE-solution-there is the desire to keep all the samples for possible later computations of similar integrals. This obviously means a lot of data. To keep the storage demands low, and to allow evaluation of the integrand at points which were not sampled, we construct a low-rank tensor approximation of the integrand over the whole integration domain. This can also be viewed as a representation in some problem-dependent basis which allows a sparse representation. What one obtains is sometimes called a "surrogate" or "proxy" model, or a "response surface". This representation is built step by step or sample by sample, and can already be used for each new sample. In case we are sampling a solution of an SPDE, this allows us to reduce the number of necessary samples, namely in case the solution is already well-represented by the low-rank tensor approximation. This can be easily checked by evaluating the residuum of the PDE with the approximate solution. The procedure will be demonstrated in the computation of a compressible transonic Reynolds-averaged Navier-Strokes flow around an airfoil with random/uncertain data. © Springer-Verlag Berlin Heidelberg 2013.en
dc.publisherSpringer Science + Business Mediaen
dc.titleSampling and Low-Rank Tensor Approximation of the Response Surfaceen
dc.typeConference Paperen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalSpringer Proceedings in Mathematics & Statisticsen
dc.conference.date13 February 2012 through 17 February 2012en
dc.conference.name10th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, MCQMC 2012en
dc.conference.locationSydney, NSWen
dc.contributor.institutionInstitute for Scientific Computing, Technische Universität Braunschweig, Hans-Sommerstr. 65, Brunswick, Germanyen
dc.contributor.institutionMIT, Cambridge, MA, United Statesen
kaust.authorLitvinenko, Alexanderen
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