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

Journal Article · Sun Jun 15 00:00:00 EDT 2014 · Journal of Computational Physics

DOI:https://doi.org/10.1016/J.JCP.2014.02.024· OSTI ID:22314869

Peng, Ji ^[1]; Hampton, Jerrad ^[2]; Doostan, Alireza ^[2]

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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)

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.

• OSTI ID: 22314869
• Journal Information: Journal of Computational Physics, Vol. 267; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

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