Global sensitivity analysis for models with spatially dependent outputs

Amandine Marrel (1) , Bertrand Iooss (2, 3) , Michel Jullien (4) , Béatrice Laurent (5) , Elena Volkova (6)

1 IFPEN - IFP Energies nouvelles
2 GdR MASCOT-NUM - Méthodes d'Analyse Stochastique des Codes et Traitements Numériques
3 EDF - EDF
4 LMTE - Laboratoire de Modélisation des Transferts dans l'Environnement
5 IMT - Institut de Mathématiques de Toulouse UMR5219
6 Institute of Nuclear Reactors

The global sensitivity analysis of a complex numerical model often requires the estimation of variance-based importance measures, called Sobol' indices. Metamodel-based techniques have been developed in order to replace the cpu time expensive computer code with an inexpensive mathematical function, predicting the computer code output. The common metamodel-based sensitivity analysis methods are appropriate with computer codes having scalar model output. However, in the environmental domain, as in many areas of application, numerical models often give as output a spatial map, which is sometimes a spatio-temporal evolution, of some interest variables. In this paper, we introduce a novel way to obtain a spatial map of Sobol' indices with a minimal number of numerical model computations. It is based on the functional decomposition of the spatial output onto a wavelet basis and the metamodeling of the wavelet coefficients by Gaussian process. An analytical example allows us to clarify the various steps of our methodology. This technique is then applied to a real case of hydrogeological modeling: for each model input variable, a spatial map of Sobol' indices is thus obtained.

Mots clés: Computer experiment; Gaussian process; metamodel; functional data; radionuclide migration

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Amandine Marrel, Bertrand Iooss, Michel Jullien, Béatrice Laurent, Elena Volkova. Global sensitivity analysis for models with spatially dependent outputs. 2010. ⟨hal-00430171v2⟩