Metamodel-based sensitivity analysis: Polynomial chaos expansions and Gaussian processes

TL;DR

This paper reviews metamodel-based methods, specifically polynomial chaos expansions and Gaussian processes, for efficient global sensitivity analysis, highlighting their strengths, limitations, and comparative performance on benchmarks and an engineering case.

Contribution

It introduces and compares PCE and GP techniques for sensitivity analysis, emphasizing their analytical and confidence interval computations, respectively, in the context of complex models.

Findings

PCE allows analytical computation of Sobol' indices from coefficients.

GP provides straightforward confidence intervals for sensitivity indices.

Both methods perform well on benchmarks and a real engineering problem.

Abstract

Global sensitivity analysis is now established as a powerful approach for determining the key random input parameters that drive the uncertainty of model output predictions. Yet the classical computation of the so-called Sobol' indices is based on Monte Carlo simulation, which is not affordable when computationally expensive models are used, as it is the case in most applications in engineering and applied sciences. In this respect metamodels such as polynomial chaos expansions (PCE) and Gaussian processes (GP) have received tremendous attention in the last few years, as they allow one to replace the original, taxing model by a surrogate which is built from an experimental design of limited size. Then the surrogate can be used to compute the sensitivity indices in negligible time. In this chapter an introduction to each technique is given, with an emphasis on their strengths and limitations in the context of global sensitivity analysis. In particular, Sobol' (resp. total Sobol') indices can be computed analytically from the PCE coefficients. In contrast, confidence intervals on sensitivity indices can be derived straightforwardly from the properties of GPs. The performance of the two techniques is finally compared on three well-known analytical benchmarks (Ishigami, G-Sobol and Morris functions) as well as on a realistic engineering application (deflection of a truss structure).