A non-adapted sparse approximation of PDEs with stochastic inputs

Authors:
Alireza Doostan;Houman Owhadi
Affiliations:
Aerospace Engineering Sciences Department, University of Colorado, Boulder, CO 80309, USA;Applied & Computational Mathematics Department, California Institute of Technology, Pasadena, CA 91125, USA
Venue:
Journal of Computational Physics
Year:
2011

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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.