Abstract
arXiv:2605.22845v1 Announce Type: cross Abstract: Finite element simulations of large-deformation sheet material forming involve node-element coupling between nodal kinematics and element-level deformation measures. Machine-learning surrogates can accelerate such simulations, but most graph-based models use node-centred representations. This representation is indirect for element-level quantities, which are often recovered from nodal predictions by interpolation or post-processing. It may also obscure the node-element coupling structure that underlies the finite element update. This work proposes a cross-attention-based bipartite graph neural network (CAtt-BiGNN) for coupled prediction of nodal displacement increments and elemental thinning. The graph represents mesh nodes and elements as distinct but connected entities, linked by directed node-element edges, so that nodal and elemental fields are predicted on their native discretisation domains. An edge-aware cross-attention processor conditions adaptive node-element coupling weights on geometric edge features, enabling bidirectional message passing between nodal kinematic states and elemental deformation states. A hierarchical extension, CAtt-BiUGNN, combines the CAtt-BiGNN with graph downsampling-upsampling to improve information propagation on larger meshes. Adaptive Gaussian noise is further evaluated as an optional rollout-stabilisation strategy. The models are tested on two representative forming cases with different graph sizes. CAtt-BiGNN improves the balance between displacement and thinning prediction relative to node-centred baselines and bipartite ablation variants, while CAtt-BiUGNN gives the strongest overall performance in the larger-graph setting. The results indicate that the proposed model provides an effective surrogate framework for large-deformation sheet material forming.