Basis adaptive sample efficient polynomial chaos (BASE-PC)

Hampton, Jerrad; Doostan, Alireza

doi:10.1016/j.jcp.2018.03.035

Title: Basis adaptive sample efficient polynomial chaos (BASE-PC)

Journal Article · 03 April 2018 · Journal of Computational Physics

DOI: https://doi.org/10.1016/j.jcp.2018.03.035 · OSTI ID:1610853

Hampton, Jerrad ^[1]; Doostan, Alireza ^[2]

Univ. of Colorado, Boulder, CO (United States); DOE/OSTI
Univ. of Colorado, Boulder, CO (United States)

For a large class of orthogonal basis functions, there has been a recent identification of expansion methods for computing accurate, stable approximations of a quantity of interest. Here this paper presents, within the context of uncertainty quantification, a practical implementation using basis adaptation, and coherence motivated sampling, which under assumptions has satisfying guarantees. This implementation is referred to as Basis Adaptive Sample Efficient Polynomial Chaos (BASE-PC). A key component of this is the use of anisotropic polynomial order which admits evolving global bases for approximation in an efficient manner, leading to consistently stable approximation for a practical class of smooth functionals. This fully adaptive, non-intrusive method, requires no a priori information of the solution, and has satisfying theoretical guarantees of recovery. A key contribution to stability is the use of a presented correction sampling for coherence-optimal sampling in order to improve stability and accuracy within the adaptive basis scheme. Theoretically, the method may dramatically reduce the impact of dimensionality in function approximation, and numerically the method is demonstrated to perform well on problems with dimension up to 1000.

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Research Organization:: Univ. of Colorado, Boulder, CO (United States)

Sponsoring Organization:: National Science Foundation (NSF); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: SC0006402

OSTI ID:: 1610853

Journal Information:: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: C Vol. 371; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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Sliced-Inverse-Regression--Aided Rotated Compressive Sensing Method for Uncertainty Quantification Yang, Xiu; Li, Weixuan; Tartakovsky, Alexandre SIAM/ASA Journal on Uncertainty Quantification, Vol. 6, Issue 4 https://doi.org/10.1137/17m1148955	journal	January 2018
Automatic selection of basis-adaptive sparse polynomial chaos expansions for engineering applications Lüthen, Nora; Marelli, Stefano; Sudret, Bruno arXiv https://doi.org/10.48550/arxiv.2009.04800	preprint	January 2020

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Title: Basis adaptive sample efficient polynomial chaos (BASE-PC)

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