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Data-driven polynomial chaos expansions: A weighted least-square approximation
Guo, Ling1; Liu, Yongle2; Zhou, Tao3
AbstractIn this work, we combine the idea of data-driven polynomial chaos expansions with the weighted least-square approach to solve uncertainty quantification (UQ) problems. The idea of data-driven polynomial chaos is to use statistical moments of the input random variables to develop an arbitrary polynomial chaos expansion, and then use such data-driven bases to perform UQ computations. Here we adopt the bases construction procedure by following (Ahlfeld et al. (2016), [1]), where the bases are computed by using matrix operations on the Hankel matrix of moments. Different from previous works, in the postprocessing part, we propose a weighted least-squares approach to solve UQ problems. This approach includes a sampling strategy and a least-squares solver. The main features of our approach are two folds: On one hand, our sampling strategy is independent of the random input. More precisely, we propose to sampling with the equilibrium measure, and this measure is also independent of the data-driven bases. Thus, this procedure can be done in prior (or in a off-line manner). On the other hand, we propose to solve a Christoffel function weighted least-square problem, and this strategy is quasi-linearly stable - the required number of PDE solvers depends linearly (up to a logarithmic factor) on the number of (data-driven) bases. This new approach is thus promising in dealing with a class of problems with epistemic uncertainties. A number of numerical tests are presented to show the effectiveness of our approach. (C) 2019 Elsevier Inc. All rights reserved.
KeywordUncertainty quantification Data-driven polynomial chaos expansions Weighted least-squares Equilibrium measure
Funding ProjectNSFC[11822111] ; NSFC[11688101] ; NSFC[91630312] ; NSFC[91630203] ; NSFC[11571351] ; NSFC[11731006] ; NSFC[11671265] ; Program for Outstanding Academic leaders in Shanghai[151503100] ; science challenge project[TZ2018001] ; national key basic research program[2018YFB0704304] ; NCMIS ; youth innovation promotion association (CAS)
WOS Research AreaComputer Science ; Physics
WOS SubjectComputer Science, Interdisciplinary Applications ; Physics, Mathematical
WOS IDWOS:000458147100008
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Document Type期刊论文
Corresponding AuthorZhou, Tao
Affiliation1.Shanghai Normal Univ, Dept Math, Shanghai, Peoples R China
2.Southern Univ Sci & Technol, Dept Math, Shenzhen, Peoples R China
3.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, LSEC, Beijing, Peoples R China
Recommended Citation
GB/T 7714
Guo, Ling,Liu, Yongle,Zhou, Tao. Data-driven polynomial chaos expansions: A weighted least-square approximation[J]. JOURNAL OF COMPUTATIONAL PHYSICS,2019,381:129-145.
APA Guo, Ling,Liu, Yongle,&Zhou, Tao.(2019).Data-driven polynomial chaos expansions: A weighted least-square approximation.JOURNAL OF COMPUTATIONAL PHYSICS,381,129-145.
MLA Guo, Ling,et al."Data-driven polynomial chaos expansions: A weighted least-square approximation".JOURNAL OF COMPUTATIONAL PHYSICS 381(2019):129-145.
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