Cross-attention-based bipartite graph neural network for coupled nodal and elemental field prediction in large-deformation sheet material forming

2026-05-14

AI Summary

Traditional explicit-dynamics finite element simulations incur high computational costs in large-deformation sheet metal forming design, hindering efficient manufacturability assessment. This work proposes the CAttBiGNN model, which—within a graph learning framework—explicitly encodes the node-element bipartite structure and introduces geometry-aware edge embeddings combined with a cross-attention mechanism to jointly predict nodal displacement increments and elemental deformation states, enabling autoregressive roll-out inference. To enhance long-range information propagation in large-scale meshes, the authors further integrate graph downsampling and upsampling strategies to construct CAttBiUGNN. Evaluated on cold stamping dome and hot forming corner benchmarks, the model significantly outperforms node-centric baselines and ablated variants, achieving improved accuracy and balance in predicting both displacements and thinning, thereby facilitating efficient design space exploration.

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.

Problem

• large-deformation sheet forming
• manufacturability assessment
• finite element simulation
• graph neural networks
• design space exploration

Innovation

• bipartite graph neural network
• finite element-inspired simulator
• cross-attention mechanism
• large-deformation forming
• manufacturability assessment