A hybrid numerical framework combining graph neural networks & classical reduced-order models for finite element systems in dynamics

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.