Global sensitivity analysis based on high-dimensional sparse surrogate construction

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.