Substitution de modèle et approche multifidélité en expérimentation numérique

De Lozzo, Matthias

Journal de la société française de statistique, Tome 156 (2015) no. 4, pp. 21-55.

Cet article présente une synthèse bibliographique sur la substitution de modèle en expérimentation numérique où l’objectif est d’approcher un simulateur numérique à partir de quelques unes de ses évaluations. Les principaux modèles de substitution y sont décrits : réseaux de neurones artificiels, modèles par processus gaussien, machines à vecteurs de support et polynômes de chaos. Des éléments d’apprentissage statistique sont par ailleurs exposés afin de choisir la complexité et les paramètres d’un modèle de substitution permettant une bonne approximation du simulateur numérique. Une ouverture à la modélisation multifidélité est proposée afin de tenir compte de sources d’observations complémentaires lorsque l’évaluation du simulateur est trop coûteuse.

This article presents a review of research literature on surrogate modeling in the context of computer experimentation where the goal is to approach a numerical simulator from some evaluations. The main surrogate models are described: artificial neural networks, gaussian process models, support vector machines and polynomial chaos expansions. Elements of statistical learning are expounded in order to select the complexity and the parameters of a surrogate model which assure a good approximation of the numerical simulator. An extension to multifidelity modelization is also proposed so as to take into account complementary sources of observations when the simulator evaluation is too expensive.

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