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A hybrid numerical framework combining graph neural networks & classical reduced-order models for finite element systems in dynamics
1 : Laboratoire de Mécanique Paris-Saclay
(LMPS)
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Site web
* : Auteur correspondant
CentraleSupélec, Université Paris-Saclay, Centre National de la Recherche Scientifique, Ecole Normale Supérieure Paris-Saclay, Centre National de la Recherche Scientifique : UMR9026
4 avenue des sciences / 8-10 rue Joliot Curie, 91190 Gif-sur-Yvette -
France
This contribution presents recent work on building a hybrid Graph Neural Network (GNN)-based reduced-order modeling framework for solving time-dependent partial differential equations on non-parametric geometries. The method exploits graph learning to predict reduced bases in a lightweight architecture that embeds finite element operators, geodesic subspace distance measures, and Gated Recurrent Units (GRUs). A new “Boosted PGD” enrichment step provides fast, on-the-fly error correction. Efficacy is demonstrated on datasets containing wide topological variations and discretization sizes.
