A GENERAL FRAMEWORK FOR ENHANCING SPARSITY OF GENERALIZED POLYNOMIAL CHAOS EXPANSIONS

Journal Article · Sat Mar 02 00:00:00 EST 2019 · International Journal for Uncertainty Quantification

DOI:https://doi.org/10.1615/Int.J.UncertaintyQuantification.2019027864· OSTI ID:1687382

Yang, Xiu  ^[1]; Wan, Xiaoliang ^[2]; Lin, Lin ^[3]; Lei, Huan ^[1]

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1. BATTELLE (PACIFIC NW LAB)
2. Louisiana State University
3. University of California, Berkeley

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.

• Research Organization: Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
• Sponsoring Organization: USDOE
• DOE Contract Number: AC05-76RL01830
• OSTI ID: 1687382
• Report Number(s): PNNL-SA-137633
• Journal Information: International Journal for Uncertainty Quantification, Vol. 9, Issue 3
• Country of Publication: United States
• Language: English