Global sensitivity analysis of computer models with functional inputs

TL;DR

This paper extends global sensitivity analysis techniques to models with functional inputs, using joint modeling of mean and dispersion to efficiently estimate sensitivity indices for complex computer codes.

Contribution

It introduces a joint modeling approach with GLMs or GAMs for sensitivity analysis of models with functional inputs, applicable to large computational codes.

Findings

Joint modeling effectively estimates sensitivity indices for functional inputs.

The approach compares favorably with classical methods on analytical functions.

Applied successfully to nuclear fuel irradiation simulation code.

Abstract

Global sensitivity analysis is used to quantify the influence of uncertain input parameters on the response variability of a numerical model. The common quantitative methods are applicable to computer codes with scalar input variables. This paper aims to illustrate different variance-based sensitivity analysis techniques, based on the so-called Sobol indices, when some input variables are functional, such as stochastic processes or random spatial fields. In this work, we focus on large cpu time computer codes which need a preliminary meta-modeling step before performing the sensitivity analysis. We propose the use of the joint modeling approach, i.e., modeling simultaneously the mean and the dispersion of the code outputs using two interlinked Generalized Linear Models (GLM) or Generalized Additive Models (GAM). The ``mean'' model allows to estimate the sensitivity indices of each scalar input variables, while the ``dispersion'' model allows to derive the total sensitivity index of the functional input variables. The proposed approach is compared to some classical SA methodologies on an analytical function. Lastly, the proposed methodology is applied to a concrete industrial computer code that simulates the nuclear fuel irradiation.