A non-adapted sparse approximation of PDEs with stochastic inputs
Numerical Analysis
2015-05-19 v1 Analysis of PDEs
Abstract
We propose a method for the approximation of solutions of PDEs with stochastic coefficients based on the direct, i.e., non-adapted, sampling of solutions. This sampling can be done by using any legacy code for the deterministic problem as a black box. The method converges in probability (with probabilistic error bounds) as a consequence of sparsity and a concentration of measure phenomenon on the empirical correlation between samples. We show that the method is well suited for truly high-dimensional problems (with slow decay in the spectrum).
Cite
@article{arxiv.1006.2151,
title = {A non-adapted sparse approximation of PDEs with stochastic inputs},
author = {Alireza Doostan and Houman Owhadi},
journal= {arXiv preprint arXiv:1006.2151},
year = {2015}
}