Enhancing l1-minimization estimates of polynomial chaos expansions using basis selection

JOURNAL OF COMPUTATIONAL PHYSICS

卷:289

Article

Jakeman, J. D.¹  Eldred, M. S.¹  Sargsyan, K.² 

[1] Sandia Natl Labs, Albuquerque, NM 87185 USA

[2] Sandia Natl Labs, Livermore, CA 94550 USA

关键词: Uncertainty quantification;    Stochastic collocation;    Polynomial chaos;    l(1)-minimization;    Sparsity;    Adaptivity;    Basis selection;   

DOI  :  10.1016/j.jcp.2015.02.025

来源: Elsevier

【 摘 要 】

In this paper we present a basis selection method that can be used with l(1)-minimization to adaptively determine the large coefficients of polynomial chaos expansions (PCE). The adaptive construction produces anisotropic basis sets that have more terms in important dimensions and limits the number of unimportant terms that increase mutual coherence and thus degrade the performance of l(1)-minimization. The important features and the accuracy of basis selection are demonstrated with a number of numerical examples. Specifically, we show that for a given computational budget, basis selection produces a more accurate PCE than would be obtained if the basis were fixed a priori. We also demonstrate that basis selection can be applied with non-uniform random variables and can leverage gradient information. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free