Non-intrusive low-rank separated approximation of high-dimensional stochastic models
KAUST Grant NumberAEA 48803
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AbstractThis 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.
CitationDoostan A, Validi A, Iaccarino G (2013) Non-intrusive low-rank separated approximation of high-dimensional stochastic models. Computer Methods in Applied Mechanics and Engineering 263: 42–55. Available: http://dx.doi.org/10.1016/j.cma.2013.04.003.
SponsorsThe work of AD and AV was partially supported by the Department of Energy under Advanced Scientific Computing Research Early Career Research Award DE-SC0006402, the National Science Foundation grant DMS-1228359, and the Predictive Science Academic Alliance Program (PSAAP) at Stanford University. GI gratefully acknowledges financial support from KAUST under award AEA 48803.