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.

翻译：大变形板料成形的有限元模拟涉及节点运动学与单元级变形度量之间的节点-单元耦合。机器学习替代模型可加速此类模拟，但多数基于图的模型采用以节点为中心的表达方式。这种表达方式对于单元级量而言是间接的——这些量通常需通过插值或后处理从节点预测中恢复，并可能掩盖有限元更新所依赖的节点-单元耦合结构。本文提出一种基于交叉注意力的二分图神经网络（CAtt-BiGNN），用于节点位移增量与单元减薄量的耦合预测。该图将网格节点与单元视为独立但相互关联的实体，通过有向节点-单元边连接，从而在各自的原生离散域上预测节点场与单元场。边感知交叉注意力处理器根据几何边特征自适应调节节点-单元耦合权重，实现节点运动状态与单元变形状态间的双向消息传递。其层次化拓展模型CAtt-BiUGNN将CAtt-BiGNN与图降采样-升采样结合，以改善较大网格上的信息传播。进一步地，自适应高斯噪声作为可选的滚动预测稳定策略被评估。模型在两种具有不同图规模的代表性成形案例上进行测试。与以节点为基准的基线模型及二分图消融变体相比，CAtt-BiGNN提升了位移与减薄预测之间的平衡性；而在大图场景下，CAtt-BiUGNN展现了最优的整体性能。结果表明，本文模型为大变形板料成形提供了有效的替代框架。