Global sensitivity analysis based on high-dimensional sparse surrogate construction

作     者：Jun HU Shudao ZHANG 

作者机构：Institute of Applied Physics and Computational Mathematics 

出 版 物：《Applied Mathematics and Mechanics(English Edition)》 (应用数学和力学（英文版）)

年 卷 期：2017年第38卷第6期

页      面：797-814页

核心收录：

学科分类：02[经济学] 0202[经济学-应用经济学] 020208[经济学-统计学] 080704[工学-流体机械及工程] 07[理学] 080103[工学-流体力学] 08[工学] 0807[工学-动力工程及工程热物理] 0714[理学-统计学（可授理学、经济学学位）] 070103[理学-概率论与数理统计] 0701[理学-数学] 0801[工学-力学（可授工学、理学学位）] 

基　　金：Project supported by the National Natural Science Foundation of China(Nos.11172049 and11472060) the Science Foundation of China Academy of Engineering Physics(Nos.2015B0201037and 2013A0101004) 

主　　题：global sensitivity analysis (GSA) curse of dimensionality sparse surrogate construction polynomial chaos (PC) compressive sensing 

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 reconstruc- tion 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.