Global sensitivity analysis based on high-dimensional sparse surrogate construction

doi:10.1007/s10483-017-2208-8

Applied Mathematics and Mechanics (English Edition) ›› 2017, Vol. 38 ›› Issue (6): 797-814.doi: https://doi.org/10.1007/s10483-017-2208-8

Global sensitivity analysis based on high-dimensional sparse surrogate construction

Jun HU, Shudao ZHANG

Institute of Applied Physics and Computational Mathematics, Beijing 100094, China

收稿日期:2016-04-20 修回日期:2016-09-25 出版日期:2017-06-01 发布日期:2017-06-01
通讯作者: Jun HU E-mail:hu_jun@iapcm.ac.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Nos. 11172049 and 11472060) and the Science Foundation of China Academy of Engineering Physics (Nos. 2015B0201037 and 2013A0101004)

Global sensitivity analysis based on high-dimensional sparse surrogate construction

Jun HU, Shudao ZHANG

Institute of Applied Physics and Computational Mathematics, Beijing 100094, China

Received:2016-04-20 Revised:2016-09-25 Online:2017-06-01 Published:2017-06-01
Contact: Jun HU E-mail:hu_jun@iapcm.ac.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Nos. 11172049 and 11472060) and the Science Foundation of China Academy of Engineering Physics (Nos. 2015B0201037 and 2013A0101004)

摘要/Abstract

摘要：

Surrogate models are usually used to perform global sensitivity analysis (GSA) by avoiding a large ensemble of deterministic simulations of the Monte Carlo method to provide a reliable estimate of GSA indices. However, most surrogate models such as polynomial chaos (PC) expansions suffer from the curse of dimensionality due to the high-dimensional input space. Thus, sparse surrogate models have been proposed to alleviate the curse of dimensionality. In this paper, three techniques of sparse reconstruction are used to construct sparse PC expansions that are easily applicable to computing variance-based sensitivity indices (Sobol indices). These are orthogonal matching pursuit (OMP), spectral projected gradient for L₁ minimization (SPGL1), and Bayesian compressive sensing with Laplace priors. By computing Sobol indices for several benchmark response models including the Sobol function, the Morris function, and the Sod shock tube problem, effective implementations of high-dimensional sparse surrogate construction are exhibited for GSA.

关键词: finite deformable, polar elastic media, dynamical equations, global sensitivity analysis (GSA), compressive sensing, curse of dimensionality, sparse surrogate construction, polynomial chaos (PC)

Abstract:

Key words: finite deformable, polar elastic media, dynamical equations, global sensitivity analysis (GSA), curse of dimensionality, sparse surrogate construction, polynomial chaos (PC), compressive sensing

中图分类号:

90C31
62J12

Jun HU, Shudao ZHANG. Global sensitivity analysis based on high-dimensional sparse surrogate construction[J]. Applied Mathematics and Mechanics (English Edition), 2017, 38(6): 797-814.

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Global sensitivity analysis based on high-dimensional sparse surrogate construction

Global sensitivity analysis based on high-dimensional sparse surrogate construction

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