Cross-attention-based bipartite graph neural network for coupled nodal and elemental field prediction in large-deformation sheet material forming
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917522327994368 |
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| author | Zhao, Yingxue Li, Haoran Zhou, Haosu Pfaff, Tobias Li, Nan |
| author_facet | Zhao, Yingxue Li, Haoran Zhou, Haosu Pfaff, Tobias Li, Nan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_22845 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Cross-attention-based bipartite graph neural network for coupled nodal and elemental field prediction in large-deformation sheet material forming Zhao, Yingxue Li, Haoran Zhou, Haosu Pfaff, Tobias Li, Nan Computational Engineering, Finance, and Science Machine Learning 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. |
| title | Cross-attention-based bipartite graph neural network for coupled nodal and elemental field prediction in large-deformation sheet material forming |
| topic | Computational Engineering, Finance, and Science Machine Learning |
| url | https://arxiv.org/abs/2605.22845 |