Méthodes d'interpolation à noyaux pour l'approximation de fonctions type boîte noire coûteuses

Abstract : This work is in the field of computer experiment which is the natural context when physical experiments are impracticable. A computer experiment consists of an evaluation of an expensive black-box function which describes a physical model. The input variables are treated as a random vector since they suffer from uncertainties. This implies that the outputs of the model which are focused on, are random. In order to make statistical analyses tractable, the black-box function can be replaced with a metamodel which approximates it and is fast to compute. We especially focus on metamodeling with kernel interpolation and the use of these metamodels. In this context, the first contribution consists of proposing a more general definition of a conditionally positive definite kernel which allows a full generalization of the concept of positive definite kernel and its associated theorems. We provide, in a second contribution, an algorithm to obtain numerical designs of experiments according to a maximin criterion which is sensible for these metamodels. In a third contribution, an inverse statistical problem is treated by using a kernel interpolation metamodel into a stochastic EM algorithm since the outputs depend on the inputs through an expensive black-box model. In the last contribution, we propose two strategies relying also on such a metamodel to estimate and to upper bound the probability of rare events based on the outputs of an expensive black-box function.
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Mathématiques [math]. Université Paris Sud - Paris XI, 2010. Français
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Pierre Barbillon. Méthodes d'interpolation à noyaux pour l'approximation de fonctions type boîte noire coûteuses. Mathématiques [math]. Université Paris Sud - Paris XI, 2010. Français. 〈tel-00559502〉

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