Computing derivative-based global sensitivity measures using polynomial chaos expansions

Bruno Sudret (1, 2) , Chu V. Mai (2)

1 GdR MASCOT-NUM - Méthodes d'Analyse Stochastique des Codes et Traitements Numériques
2 ETH Zürich - Eidgenössische Technische Hochschule - Swiss Federal Institute of Technology [Zürich]

In the field of computer experiments sensitivity analysis aims at quantifying the relative importance of each input parameter (or combinations thereof) of a computational model with respect to the model output uncertainty. Variance decomposition methods leading to the well-known Sobol' indices are recognized as accurate techniques, at a rather high computational cost though. The use of polynomial chaos expansions (PCE) to compute Sobol' indices has allowed to alleviate the computational burden though. However, when dealing with large dimensional input vectors, it is good practice to first use screening methods in order to discard unimportant variables. The derivative-based global sensitivity measures (DGSM) have been developed recently in this respect. In this paper we show how polynomial chaos expansions may be used to compute analytically DGSMs as a mere post-processing. This requires the analytical derivation of derivatives of the orthonormal polynomials which enter PC expansions. Closed-form expressions for Hermite, Legendre and Laguerre polynomial expansions are given. The efficiency of the approach is illustrated on two well-known benchmark problems in sensitivity analysis.

Mots clés: polynomial chaos expansions; global sensitivity analysis; derivative-based global sensitivity measures; derivatives of orthonormal polynomials; Morris method; Monte Carlo simulation

Domaines: Méthodologie [stat.ME]; Calcul [stat.CO]

Bruno Sudret, Chu V. Mai. Computing derivative-based global sensitivity measures using polynomial chaos expansions. 2015. ⟨hal-01154395⟩