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International Journal for Uncertainty Quantification
Impact-faktor: 3.259 5-jähriger Impact-Faktor: 2.547 SJR: 0.531 SNIP: 0.8 CiteScore™: 1.52

ISSN Druckformat: 2152-5080
ISSN Online: 2152-5099

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International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.2019027864
pages 221-243

A GENERAL FRAMEWORK FOR ENHANCING SPARSITY OF GENERALIZED POLYNOMIAL CHAOS EXPANSIONS

Xiu Yang
Advanced Computing, Mathematics and Data Division, Pacific Northwest National Laboratory, Richland, WA, 99352
Xiaoliang Wan
Department of Mathematics and Center of Computation and Technology, Louisiana State University, Baton Rouge, LA, 70803
Lin Lin
Department of Mathematics, University of California, Berkeley and Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720
Huan Lei
Advanced Computing, Mathematics and Data Division, Pacific Northwest National Laboratory, Richland, WA, 99352

ABSTRAKT

Compressive sensing has become a powerful addition to uncertainty quantification when only limited data are available. In this paper, we provide a general framework to enhance the sparsity of the representation of uncertainty in the form of generalized polynomial chaos expansion. We use an alternating direction method to identify new sets of random variables through iterative rotations so the new representation of the uncertainty is sparser. Consequently, we increase both the efficiency and accuracy of the compressive-sensing-based uncertainty quantification method. We demonstrate that the previously developed rotation-based methods to enhance the sparsity of Hermite polynomial expansion is a special case of this general framework. Moreover, we use Legendre and Chebyshev polynomial expansions to demonstrate the effectiveness of this method with applications in solving stochastic partial differential equations and high-dimensional (O (100)) problems.

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