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Title: A weighted ℓ{sub 1}-minimization approach for sparse polynomial chaos expansions

This work proposes a method for sparse polynomial chaos (PC) approximation of high-dimensional stochastic functions based on non-adapted random sampling. We modify the standard ℓ{sub 1}-minimization algorithm, originally proposed in the context of compressive sampling, using a priori information about the decay of the PC coefficients, when available, and refer to the resulting algorithm as weightedℓ{sub 1}-minimization. We provide conditions under which we may guarantee recovery using this weighted scheme. Numerical tests are used to compare the weighted and non-weighted methods for the recovery of solutions to two differential equations with high-dimensional random inputs: a boundary value problem with a random elliptic operator and a 2-D thermally driven cavity flow with random boundary condition.
Authors:
 [1] ;  [2] ;  [2]
  1. Mechanical Engineering Department, University of Colorado, Boulder, CO 80309 (United States)
  2. Aerospace Engineering Sciences Department, University of Colorado, Boulder, CO 80309 (United States)
Publication Date:
OSTI Identifier:
22314869
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Computational Physics; Journal Volume: 267; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGORITHMS; APPROXIMATIONS; BOUNDARY CONDITIONS; BOUNDARY-VALUE PROBLEMS; CHAOS THEORY; COMPARATIVE EVALUATIONS; EXPANSION; MATHEMATICAL SOLUTIONS; MINIMIZATION; PARTIAL DIFFERENTIAL EQUATIONS; POLYNOMIALS; RANDOMNESS; STOCHASTIC PROCESSES