基于交叉注意力的二分图神经网络用于大变形板材成形中节点和单元场的耦合预测
A finite-element-inspired bipartite graph learned simulator for manufacturability assessment in large-deformation sheet forming
AI总结：
提出交叉注意力二分图神经网络（CAtt-BiGNN），通过节点-单元二分图结构和边感知交叉注意力机制，实现大变形板材成形中节点位移增量和单元减薄量的耦合预测。
摘要：
大变形板材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。机器学习代理可以加速此类模拟，但大多数基于图的模型使用以节点为中心的表示。这种表示对于单元级量是间接的，通常通过插值或后处理从节点预测中恢复。它也可能模糊有限元更新背后的节点-单元耦合结构。本文提出了一种基于交叉注意力的二分图神经网络（CAtt-BiGNN），用于节点位移增量和单元减薄量的耦合预测。该图将网格节点和单元表示为不同但相连的实体，通过有向节点-单元边连接，从而在它们本征的离散域上预测节点场和单元场。边感知交叉注意力处理器根据几何边特征自适应地调节节点-单元耦合权重，实现节点运动状态与单元变形状态之间的双向消息传递。层次化扩展CAtt-BiUGNN将CAtt-BiGNN与图下采样-上采样相结合，以改善在较大网格上的信息传播。进一步评估了自适应高斯噪声作为可选的展开稳定策略。模型在两个具有不同图尺寸的代表性成形案例上进行了测试。与以节点为中心的基线和二分消融变体相比，CAtt-BiGNN改善了位移和减薄预测之间的平衡，而CAtt-BiUGNN在较大图设置下给出了最强的整体性能。结果表明，所提出的模型为大变形板材成形提供了一个有效的代理框架。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
