A weighted L1-minimization approach for sparse polynomial chaos expansions
Abstract
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 l1 -minimization algorithm, originally proposed in the context of compressive sampling, using a priori information about the decay of the PC coefficients and refer to the resulting algorithm as weighted l1 -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.
Cite
@article{arxiv.1308.0624,
title = {A weighted L1-minimization approach for sparse polynomial chaos expansions},
author = {Ji Peng and Jerrad Hampton and Alireza Doostan},
journal= {arXiv preprint arXiv:1308.0624},
year = {2015}
}
Comments
37 pages, 10 figures