Enhancing sparsity of Hermite polynomial expansions by iterative rotations

Journal Article · Mon Feb 01 04:00:00 EST 2016 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2015.11.038· OSTI ID:1248437

Yang, Xiu; Lei, Huan; Baker, Nathan A.; Lin, Guang

Compressive sensing has become a powerful addition to uncertainty quantification in recent years. This paper identifies new bases for random variables through linear mappings such that the representation of the quantity of interest is more sparse with new basis functions associated with the new random variables. This sparsity increases both the efficiency and accuracy of the compressive sensing-based uncertainty quantification method. Specifically, we consider rotation- based linear mappings which are determined iteratively for Hermite polynomial expansions. We demonstrate the effectiveness of the new method with applications in solving stochastic partial differential equations and high-dimensional (O(100)) problems.

• Research Organization: Pacific Northwest National Laboratory (PNNL), Richland, WA (US)
• Sponsoring Organization: USDOE
• DOE Contract Number: AC05-76RL01830
• OSTI ID: 1248437
• Report Number(s): PNNL-SA-110981; KJ0401000
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 307; ISSN 0021-9991
• Publisher: Elsevier
• Country of Publication: United States
• Language: English