A weighted l(1)-minimization approach for sparse polynomial chaos expansions

作者：Peng Ji; Hampton Jerrad; Doostan Alireza^*

来源：Journal of Computational Physics, 2014, 267: 92-111.

DOI：10.1016/j.jcp.2014.02.024

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

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.

• 出版日期2014-6-15