A general framework for enhancing sparsity of generalized polynomial chaos expansions
Document Type
Article
Publication Date
1-1-2019
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 rotation-based methods 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.
Publication Source (Journal or Book title)
International Journal for Uncertainty Quantification
First Page
221
Last Page
243
Recommended Citation
Yang, X., Wan, X., Lin, L., & Lei, H. (2019). A general framework for enhancing sparsity of generalized polynomial chaos expansions. International Journal for Uncertainty Quantification, 9 (3), 221-243. https://doi.org/10.1615/Int.J.UncertaintyQuantification.2019027864