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

Alireza Doostan, AbdoulAhad Validi, Gianluca Iaccarino

Research output: Contribution to journalArticlepeer-review

62 Scopus citations

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.
Original languageEnglish (US)
Pages (from-to)42-55
Number of pages14
JournalComputer Methods in Applied Mechanics and Engineering
Volume263
DOIs
StatePublished - Aug 2013
Externally publishedYes

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