Résultats de recherche

Documents et médias Télécharger le support Résumé A broad class of problems in science and engineering involves the repeated solution of partial differential equations (PDEs) for different parameter values. Linear reduced order models are a powerful tool …

Documents et médias Télécharger le support Résumé The design of smart autonomous mechanical structures able to perform online control of their integrity, and take anticipated actions during service before downtime or failure occur, has become an active …

Documents et médias Télécharger le support Résumé  To meet the rigorous demands of Best-Estimate Plus Uncertainty (BEPU) in modern nuclear engineering, it is essential to characterize safety margins and system dynamics with both high fidelity and high …

Documents et médias Télécharger le support Résumé This talk presents the Polytope Division Method (PDM), a greedy algorithm for solving high-dimensional configuration optimization problems—such as those arising in model reduction and optimal experimental …

Résumé Multi-query simulation settings require efficient surrogates for the underlying processes. We consider a scale of kernel-based greedy schemes for approximating the solutions of PDEs, exemplified by elliptic boundary value problems [1]. The …

Documents et médias Télécharger le support Résumé Joint work with Romain Verdière (Inria Grenoble) and Olivier Zahm (Inria Grenoble). During this talk, I will present a gradient-enhanced algorithm for high-dimensional function approximation which achieves …

Documents et médias Télécharger le support Résumé Dirac-Frenkel instantaneous residual minimization evolves nonlinear parametrizations of PDE solutions in time, but ill-conditioning can render the parameter dynamics non-unique. We interpret this …

Résumé Among several recently proposed data-driven Reduced Order Models (ROMs), deep learning-based ROMs (DL-ROMs) have proved to be a successful strategy to construct non-intrusive, highly accurate surrogates for the real time solution of parametric …

Documents et médias Télécharger le support Résumé Classically, model order reduction for parameterized systems is based on a so-called offline phase, where reduced approximation spaces are constructed and the reduced parameterized system is built, …

Résumé Dans cette présentation, nous discuterons des avancées récentes en matière de jumeaux hybrides et de leurs synergies avec une intelligence artificielle informée par des biais allant de la physique et de la géométrie à la résilience. Des exemples …

Documents et médias Télécharger le support Résumé The simulation and optimization of complex technical systems often require models that are both sufficiently accurate and computationally efficient. In engineering practice, this balance is difficult to …

Documents et médias Télécharger le support Résumé Recent advances in nonlinear model reduction indicate that overcoming linear Kolmogorov limitations requires principled combinations of projection-based approximation and data-driven modeling [3]. In …

Résumé This talk addresses numerical methods for gradient flows in Hilbert spaces based on neural network approximations. The central idea is to represent the solution on a neural network manifold and evolve its parameters in time. At first glance, this …

Documents et médias Télécharger le support Résumé In this talk, I will present Collocated Model Order Reduction (cMOR), a novel hyper-reduction framework specifically designed for high-order discretizations. The method evaluates the governing operator …

Documents et médias Télécharger le support Résumé In this talk, we present a reduced basis method for the computation of the lowest eigenvalue(s) of a parametrized family of eigenvalue problems motivated by, but not restricted to, many-body quantum …

Documents et médias Télécharger le support Résumé Solving eigenvalue problems for high-dimensional Schrödinger operators is a central challenge in numerical analysis, with applications ranging from quantum mechanics to the approximation of complex …