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Abstract: We propose a method for the approximation of solutions of PDEs withstochastic coefficients based on the direct, i.e., non-adapted, sampling ofsolutions. This sampling can be done by using any legacy code for thedeterministic problem as a black box. The method converges in probability withprobabilistic error bounds as a consequence of sparsity and a concentration ofmeasure phenomenon on the empirical correlation between samples. We show thatthe method is well suited for truly high-dimensional problems with slow decayin the spectrum.



Author: Alireza Doostan, Houman Owhadi

Source: https://arxiv.org/







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