Data-driven polynomial chaos expansions: A weighted least-square approximation

doi:10.1016/j.jcp.2018.12.020

	Data-driven polynomial chaos expansions: A weighted least-square approximation
	Guo, Ling 1; Liu, Yongle 2; Zhou, Tao3
	2019-03-15
发表期刊	JOURNAL OF COMPUTATIONAL PHYSICS
ISSN	0021-9991
卷号	381 页码:129-145
摘要	In 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.
关键词	Uncertainty quantification Data-driven polynomial chaos expansions Weighted least-squares Equilibrium measure
DOI	10.1016/j.jcp.2018.12.020
语种	英语
资助项目	NSFC[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研究方向	Computer Science ; Physics
WOS类目	Computer Science, Interdisciplinary Applications ; Physics, Mathematical
WOS记录号	WOS:000458147100008
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/32408
专题	计算数学与科学工程计算研究所
通讯作者	Zhou, Tao
作者单位	1.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
推荐引用方式 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.