Décompositions tensorielles et factorisations de calculs intensifs appliquées à l'identification de modèles de comportement non linéaire

Abstract : This thesis presents a novel non-intrusive methodology to construct surrogate models of parametric physical models.The proposed methodology enables to approximate in real-time, over the entire parameter space, multiple heterogeneous quantities of interest derived from physical models.The surrogate models are based on tensor train representations built during an intensive offline computational stage.The fundamental idea of the learning stage is to construct simultaneously all tensor approximations based on a reduced number of solutions of the physical model obtained on the fly.The parsimonious exploration of the parameter space coupled with the compact tensor train representation allows to alleviate the curse of dimensionality.The approach accommodates particularly well to models involving many parameters defined over large domains.The numerical results on nonlinear elasto-viscoplastic laws show that compact surrogate models in terms of memory storage that accurately predict multiple time dependent mechanical variables can be obtained at a low computational cost.The real-time response provided by the surrogate model for any parameter value allows the implementation of decision-making tools that are particularly interesting for experts in the context of parametric studies and aim at improving the procedure of calibration of material laws.
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Clément Olivier. Décompositions tensorielles et factorisations de calculs intensifs appliquées à l'identification de modèles de comportement non linéaire. Matériaux. PSL Research University, 2017. Français. ⟨NNT : 2017PSLEM040⟩. ⟨tel-01783950⟩

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