Global sensitivity analysis for models with spatially dependent outputs

TL;DR

This paper introduces a novel wavelet-based Gaussian process metamodeling approach to efficiently compute spatially-resolved Sobol' sensitivity indices for models with spatial outputs, demonstrated on a hydrogeological case.

Contribution

The paper presents an innovative method combining wavelet decomposition and Gaussian process metamodeling to estimate spatial Sobol' indices with minimal model evaluations.

Findings

Effective spatial Sobol' index maps obtained for a hydrogeological model.

Method reduces computational cost compared to traditional approaches.

Applicable to models with spatially and temporally varying outputs.

Abstract

The global sensitivity analysis of a complex numerical model often calls for the estimation of variance-based importance measures, named Sobol' indices. Metamodel-based techniques have been developed in order to replace the cpu time-expensive computer code with an inexpensive mathematical function, which predicts the computer code output. The common metamodel-based sensitivity analysis methods are well-suited for computer codes with scalar outputs. However, in the environmental domain, as in many areas of application, the numerical model outputs are often spatial maps, which may also vary with time. In this paper, we introduce an innovative method to obtain a spatial map of Sobol' indices with a minimal number of numerical model computations. It is based upon the functional decomposition of the spatial output onto a wavelet basis and the metamodeling of the wavelet coefficients by the Gaussian process. An analytical example is presented to clarify the various steps of our methodology. This technique is then applied to a real hydrogeological case: for each model input variable, a spatial map of Sobol' indices is thus obtained.