Library Subscription: Guest
Begell Digital Portal Begell Digital Library eBooks Journals References & Proceedings Research Collections
International Journal for Uncertainty Quantification
IF: 0.967 5-Year IF: 1.301 SJR: 0.531 SNIP: 0.8 CiteScore™: 1.52

ISSN Print: 2152-5080
ISSN Online: 2152-5099

Open Access

International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.2019027864
Forthcoming Article

A General Framework for Enhancing Sparsity of Generalized Polynomial Chaos Expansions

Xiu Yang
Advanced Computing, Mathematics and Data Division, Pacific Northwest National Laboratory
Xiaoliang Wan
Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana 70803, USA
Lin Lin
Department of Mathematics, University of California, Berkeley and Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
Lei Huan
Advanced Computing, Mathematics and Data Division, Pacific Northwest National Laboratory

ABSTRACT

Compressive sensing has become a powerful addition to uncertainty quantification when only limited data are available. In this paper, we provide a general framework to enhance the sparsity of the representation of uncertainty in the form of generalized polynomial chaos expansion. We use an alternating direction method to identify new sets of random variables through iterative rotations so the new representation of the uncertainty is sparser. Consequently, we increase both the efficiency and accuracy of the compressive-sensing-based uncertainty quantification method. We demonstrate that the previously developed iterative method to enhance the sparsity of Hermite polynomial expansion is a special case of this general framework. Moreover, we use Legendre and Chebyshev polynomial expansions to demonstrate the effectiveness of this method with applications in solving stochastic partial differential equations and high-dimensional (O(100)) problems.