Global Graph Surrogates and Neural Graph Elements for Computational Mechanics

ABSTRACT Machine learning surrogates are increasingly used to accelerate physics‐based simulations by predicting full‐field responses at a fraction of the computational cost. In this contribution, we present two complementary graph‐based approaches for surrogate modelling in computational mechanics. Both methods are explicitly designed to account for boundary conditions, loading configurations, and deformation dynamics—physical aspects that existing state‐of‐the‐art graph‐based simulators do not explicitly incorporate. First, a global graph surrogate workflow is introduced for predicting the deformation of a three‐dimensional automotive bumper problem, trained on geometrically nonlinear, inelastic finite element simulation data. The proposed framework is called dynamics‐informed graph neural network (DI‐GNN), which incorporates a novel FEM‐aware attention operator (FEMAT), a geometry‐aware normalisation strategy, and physics‐guided training via gradient‐ and constitutive‐law‐based losses, achieving high predictive accuracy within the training distribution. To overcome the inherent limitations of global surrogates—namely, their tight coupling to specific geometries and loading configurations—we introduce neural graph elements (NGEs), a localised, graph‐based neural network that learn element‐level mechanical behaviour rather than structure‐specific solution fields. This modular formulation, grounded in an incremental variational framework, enables the assembly of complex structures from reusable learned elements, offering a pathway towards transferable, mesh‐robust intelligent elements and a closer integration of AI‐driven modelling with numerical methods in mechanics.