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A Non-adapted Sparse Approximation of PDEs with Stochastic Inputs

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 (Unpublished) http://resolver.caltech.edu/CaltechAUTHORS:20111012-112644923

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Abstract

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)
Related URLs:
URLURL TypeDescription
http://resolver.caltech.edu/CaltechAUTHORS:20110414-085411000OtherUNSPECIFIED
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
Funders:
Funding AgencyGrant Number
DOEUNSPECIFIED
NSFCMMI-092600
Subject Keywords:Polynomial chaos; Uncertainty quantification; Stochastic PDE; Compressive sampling; Sparse approximation
Other Numbering System:
Other Numbering System NameOther Numbering System ID
Applied & Computational Mathematics Technical Report2010-02
Record Number:CaltechAUTHORS:20111012-112644923
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20111012-112644923
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:27191
Collection:CaltechACMTR
Deposited By: Kristin Buxton
Deposited On:19 Oct 2011 19:46
Last Modified:26 Dec 2012 14:16

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