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Research

Thesis viva

Introspective meta-modeling for analyzing simulated physical phenomena. Formalization within the context of co-Kriging and algorithmic integration in optimization and inversion


Nicolas Garland will defend his thesis

on Thursday​​​ 22thoctober 2020 at 2:00 pm

at ​École des Mines of Saint-Etienne, 514 room

Espace Fauriel, 29 rue Ponchardier
42100 Saint-Étienne
France

 

Ju​ry

Céline Helbert, reporter
François Bachoc, reporter
Alain Rakotomamonjy, jury president
Rodolphe Le Riche, thesis director
Nicolas Durrande, EMSE supervisor
Jean-Antoine Désidéri
Yann Richet, invited member


Abstract
In this thesis, we aim to improve the algorithms used by safety experts to analyse the outputs of their computer simulations of physical phenomena.
Since simulations are expensive, the related algorithms build the design of experiments sequentially, using metamodels to predict the outcome of the simulations. We pay special attention to chain-produced simulations (where outputs of one code are used as inputs in other numerical simulators).
The information given by the first codes allows a so-called "introspective" analysis of the final quantity.

Firstly, we review different possible introspective metamodels, which treat the results as a multi-outputs function. We thus study the different forms of co-kriging and propose an improvement for the optimization of its hyperparameters. We also develop another introspective metamodel, the hyper-kriging. We then make a comparison between the predictive performance of these metamodels.

Secondly, we work on the algorithms. An optimization algorithm, called "Step or Stop Optimization", is developed, taking into account the specificities of the introspective case. It allows to stop the computation if the first steps are disengaging. Comparisons with currently used algorithm tend to confirm a significant saving in computing resources thanks to a better consideration of the intermediate physics of the simulation.
The strategy used in this algorithm can be generalized, and extended to be used beyond the context of optimization problems.



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