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

Guo, Ling1; Liu, Yongle2; Zhou, Tao3

2019-03-15

10.1016/j.jcp.2018.12.020

JOURNAL OF COMPUTATIONAL PHYSICS   影响因子和分区

0021-9991

1090-2716

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.

Uncertainty quantification Data-driven polynomial chaos expansions Weighted least-squares Equilibrium measure

SCI ; EI

英语

其他

national key basic research program[2018YFB0704304]

Computer Science ; Physics

Computer Science, Interdisciplinary Applications ; Physics, Mathematical

WOS:000458147100008

ACADEMIC PRESS INC ELSEVIER SCIENCE

20201708548405

Expansion ; Polynomial approximation ; Sampling ; Matrix algebra ; Uncertainty analysis

Algebra:921.1 ; Numerical Methods:921.6 ; Probability Theory:922.1 ; Materials Science:951

PHYSICS

Web of Science

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

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.

Guo, Ling,Liu, Yongle,&Zhou, Tao.(2019).Data-driven polynomial chaos expansions: A weighted least-square approximation.JOURNAL OF COMPUTATIONAL PHYSICS,381,129-145.

Guo, Ling,et al."Data-driven polynomial chaos expansions: A weighted least-square approximation".JOURNAL OF COMPUTATIONAL PHYSICS 381(2019):129-145.