# Utilisation de simulateurs multi-fidélité pour les études d'incertitudes dans les codes de caclul

#### Spécialité : Mathématiques Appliquées

8/10/2015 - 14:00 Mr Federico Zertuche Salle 1 - Tour IRMA

Mots clé :

- Gaussian Processes
- Wavelets

A very important tool used by applied mathematicians and engineers to model the behavior of a system are computer simulations. They have become increasingly more precise but also more complicated. So much, that they are very slow to produce an output and thus difficult to sample so that many aspects of these simulations are not very well understood. For example, in many cases they depend on parameters whose value is unknown. A metamodel is a reconstruction of the simulation. It requires much less time to produce an output that is close to what the simulation would. By using it, some aspects of the original simulation can be studied. It is built with very few samples and its purpose is to replace the simulation. This thesis is concerned with the construction of a metamodel in a particular context called multi-fidelity. In multi-fidelity the metamodel is constructed using the data from the target simulation along other samples that are related. These approximate samples can come from a degraded version of the simulation; an old version that has been studied extensively or another simulation in which a part of the description is simplified. By learning the difference between the samples it is possible to incorporate the information of the approximate data and this may lead to an enhanced metamodel. In this manuscript two approaches that do this are studied: one based on Gaussian process modeling and another based on a coarse to ne Wavelet decomposition. The st method shows how by estimating the relationship between two data sets it is possible to incorporate data that would be useless otherwise. In the second method an adaptive procedure to add data systematically to enhance the metamodel is proposed. The object of this work is to better our comprehension of how to incorporate approximate data to enhance a metamodel. Working with a multi-fidelity metamodel helps us to understand in detail the data that nourish it. At the end a global picture of the elements that compose it is formed: the relationship and the differences between all the data sets become clearer.

#### Directeurs:

- Mr Anestis Antoniadis
*(Professeur - Université Joseph Fourier )* - Mme Céline Helbert
*(Maître de conférence - Institut Camille Jordan )*

#### Raporteurs:

- Mr Josselin Garnier
*(Professeur - Université Paris Diderot )* - Mr Alberto Pasanisi
*(Project Manager - EDF R&D )*

#### Examinateurs:

- Mme Clémentine Prieur
*(Professeur - Université Joseph Fourier )* - Mr Fabrice Gamboa
*(Professeur - Université Paul Sabatier )* - Mr Mathieu Couplet
*(Ingénieur de Recherche - EDF R&D )*