Calculations of Sobol indices for the Gaussian process metamodel

TL;DR

This paper explores methods for calculating Sobol indices using Gaussian process metamodels to enable efficient global sensitivity analysis of complex, computationally expensive models, with a focus on two approaches and their advantages.

Contribution

It introduces and compares two methods for Sobol index estimation with Gaussian process models, highlighting the superiority of the global stochastic process approach.

Findings

The second approach shows better convergence and robustness.

The second approach provides confidence intervals for Sobol indices.

Applied successfully to hydrogeological modeling case.

Abstract

Global sensitivity analysis of complex numerical models can be performed by calculating variance-based importance measures of the input variables, such as the Sobol indices. However, these techniques, requiring a large number of model evaluations, are often unacceptable for time expensive computer codes. A well known and widely used decision consists in replacing the computer code by a metamodel, predicting the model responses with a negligible computation time and rending straightforward the estimation of Sobol indices. In this paper, we discuss about the Gaussian process model which gives analytical expressions of Sobol indices. Two approaches are studied to compute the Sobol indices: the first based on the predictor of the Gaussian process model and the second based on the global stochastic process model. Comparisons between the two estimates, made on analytical examples, show the superiority of the second approach in terms of convergence and robustness. Moreover, the second approach allows to integrate the modeling error of the Gaussian process model by directly giving some confidence intervals on the Sobol indices. These techniques are finally applied to a real case of hydrogeological modeling.