A weighted l1-minimization approach for sparse polynomial chaos expansions

JOURNAL OF COMPUTATIONAL PHYSICS

卷:267

Article

Peng, Ji¹  Hampton, Jerrad²  Doostan, Alireza² 

[1] Univ Colorado, Dept Mech Engn, Boulder, CO 80309 USA

[2] Univ Colorado, Dept Aerosp Engn Sci, Boulder, CO 80309 USA

关键词: Compressive sampling;    Sparse approximation;    Polynomial chaos;    Basis pursuit denoising (BPDN);    Weighted l(1)-minimization;    Uncertainty quantification;    Stochastic PDEs;   

DOI  :  10.1016/j.jcp.2014.02.024

来源: Elsevier

【 摘 要 】

This work proposes a method for sparse polynomial chaos (PC) approximation of high-dimensional stochastic functions based on non-adapted random sampling. We modify the standard l(1)-minimization algorithm, originally proposed in the context of compressive sampling, using a priori information about the decay of the PC coefficients, when available, and refer to the resulting algorithm as weighted l(1)-minimization. We provide conditions under which we may guarantee recovery using this weighted scheme. Numerical tests are used to compare the weighted and non-weighted methods for the recovery of solutions to two differential equations with high-dimensional random inputs: a boundary value problem with a random elliptic operator and a 2-D thermally driven cavity flow with random boundary condition. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free