A finite-element-inspired bipartite graph learned simulator for manufacturability assessment in large-deformation sheet forming

Abstract

Explicit dynamic finite element (FE) simulations are widely used for large-deformation analysis but remain expensive for design-space exploration. In explicit FE analysis, nodal kinematics and element-level deformation measures evolve through a coupled node-element update process. An FE-inspired learned simulator can preserve this structure and learn nodal kinematics and elemental deformation on their native domains. Nodal displacement describes geometry evolution, while elemental thinning identifies local deformation and critical regions. Feeding both outputs back during rollout allows each field to inform subsequent updates of the other. This work proposes CAtt-BiGNN, a cross-attention-based bipartite graph neural network for coupled nodal-elemental learning. The bipartite graph encodes FE-guided state organisation and information flow without imposing equilibrium or constitutive constraints. Mesh nodes and elements are represented as distinct graph entities connected by directed node-element edges, enabling prediction of nodal displacement increments and elemental deformation on their native domains. An edge-aware cross-attention processor dynamically updates edge representations and weights messages using the receiving state and evolving local relations. For larger graphs, CAtt-BiUGNN uses separate nodal and elemental downsampling and upsampling to enhance long-range propagation while preserving their interaction across graph levels. The method is evaluated on dome-shaped cold-forming and corner-shaped hot-forming benchmarks. Comparisons with node-centred baselines, an FE-inspired hypergraph model, a Physics-Attention-based neural operator, a graph Transformer, and attention ablations show improved joint accuracy in nodal displacement and elemental thinning prediction during autoregressive rollout.