Doostan, Alireza and Owhadi, Houman (2010) A Non-adapted Sparse Approximation of PDEs with Stochastic Inputs. California Institute of Technology , Pasadena, CA. (Unpublished) http://resolver.caltech.edu/CaltechAUTHORS:20111012-112644923
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We propose a method for the approximation of solutions of PDEs with stochastic coefficients based on the direct non-adapted, 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).
|Item Type:||Report or Paper (Technical Report)|
|Additional Information:||Preprint submitted to Elsevier The first author acknowledges the support of the United States Department of Energy under Stanford’s Predictive Science Academic Alliance Program (PSAAP) for the preliminary stages of his work. The second author acknowledges the support of the National Science Foundation via NSF grant CMMI- 092600 and of the United States Department of Energy under Caltech’s Predictive Science Academic Alliance Program (PSAAP).|
|Group:||Applied & Computational Mathematics|
|Subject Keywords:||Polynomial chaos; Uncertainty quantification; Stochastic PDE; Compressive sampling; Sparse approximation|
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|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Kristin Buxton|
|Deposited On:||19 Oct 2011 19:46|
|Last Modified:||26 Dec 2012 14:16|
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