Thèse de DOCTORAT
Spécialité: Mathématiques Appliquées
Mr Federico ZERTUCHE
soutiendra le Jeudi 8 Octobre 2015 à 14h00 Salle 1  Tour IRMA
Titre:Utilisation de simulateurs multifidélité pour les études d'incertitudes dans les codes de caclul
Ces travaux se sont déroulés sous la direction de Mr Anestis ANTONIADIS (Professeur, Université Joseph Fourier) et de Mme Céline HELBERT (Maître de conférence, Institut Camille Jordan)
Résumé:
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 dicult 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 multidelity. In multidelity 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 a another simulation in which a part of the description is simplied.
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
multidelity 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.
MotsClés:
Regression, Gaussian Processes, Wavelets
Membres du Jury:
Rapporteurs:
Mr Josselin GARNIER (Professeur, Université Paris Diderot)
Mr Alberto PASANISI (Project Manager, EDF R&D)
Examinateurs:
Mme Clémentine PRIEUR (Professeur, Université Joseph Fourier)
Mr Mathieu COUPLET (Ingénieur de Recherche, EDF R&D)
Mr Fabrice GAMBOA (Professeur, Université Paul Sabatier)
(sans cadre)
