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

Fabio Nobile, Raul Tempone, Sören Wolfers

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

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.
Original languageEnglish (US)
Pages (from-to)247-280
Number of pages34
JournalNumerische Mathematik
Volume139
Issue number1
DOIs
StatePublished - Nov 16 2017

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