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arXiv · 1308.0624

A weighted L1-minimization approach for sparse polynomial chaos expansions

Ji Peng·Jerrad Hampton·Alireza Doostan
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Abstract

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 l1 -minimization algorithm, originally proposed in the context of compressive sampling, using a priori information about the decay of the PC coefficients and refer to the resulting algorithm as weighted l1 -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.

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Ji Peng, Jerrad Hampton, Alireza Doostan. 2013-08-02. A weighted L1-minimization approach for sparse polynomial chaos expansions. https://doi.org/10.1016/j.jcp.2014.02.024

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