arXiv:2605.22845cs.CEcs.LG2026-05

用图神经网络模拟大变形钣金成形,提升设计优化效率。

A finite-element-inspired bipartite graph learned simulator for manufacturability assessment in large-deformation sheet forming

论文配图:A finite-element-inspired bipartite graph learned simulator for manufacturability assessment in large-deformation sheet forming
图 1 · 摘自论文原文
  • 构建节点-单元双分图模型,直接建模节点位移与单元变形。
  • 在冷/热成形基准上预测精度优于基线模型,位移和减薄误差更小。
  • 适合需要快速评估成形可制造性的工程师与算法研究者。

显式动态有限元(FE)仿真广泛用于大变形工程分析,但在设计空间探索与优化中重复计算成本高。在显式FE分析中,节点运动与单元层面的变形通过耦合的节点-单元更新演化。这启发了基于图的代理仿真器,用于近似单步FE状态转移并自回归展开。然而,许多基于网格的图代理以节点为中心,难以直接表示单元级变量及节点-单元间原生信息交换。本文提出CAttBiGNN,一种基于交叉注意力的双分图神经网络,用于耦合节点-单元学习。图结构将FE网格的节点与单元作为独立实体,通过有向节点-单元边连接,使节点位移增量与单元级变形状态在其原始离散域上得以预测。边缘感知的交叉注意力处理器利用几何边嵌入调节方向性消息传递。对于更大规模图,CAttBiUGNN结合图下采样与上采样策略,提升远距离信息传播能力。方法在圆顶状冷成形与角状热成形基准上评估。与节点中心基线及双分图、注意力模块消融实验对比显示,在自回归展开过程中,节点位移与单元减薄预测的准确性和平衡性均显著提升。结果表明,所提出的有限元启发式学习模拟器可支持面向可制造性的场预测与高效设计空间探索。

原文摘要 · Abstract (English)

Explicit dynamic finite element (FE) simulations are widely used for large deformation engineering analysis, but repeated simulations remain costly during design space exploration and optimisation. In explicit FE analysis, nodal kinematics and element level deformation measures evolve through coupled node element updates. This motivates graph learned simulators that approximate one step FE state transitions and roll them out autoregressively. However, many mesh based graph surrogates are node centred, which makes element level variables and native nodal elemental exchange less direct to represent. This work proposes CAttBiGNN, a cross attention based bipartite graph neural network for coupled nodal elemental learning. The graph represents FE mesh nodes and elements as distinct entities linked by directed node element edges, enabling nodal displacement increments and element level deformation states to be predicted on their native discretisation domains. An edge aware cross attention processor uses geometric edge embeddings to modulate directional node element message passing. For larger graphs, CAttBiUGNN combines the bipartite processor with graph downsampling and upsampling to improve long-range information propagation. The method is evaluated on dome shaped cold forming and corner shaped hot forming benchmarks. Comparisons with node centred baselines and bipartite and attention ablations show improved accuracy and balance in nodal displacement and elemental thinning prediction during autoregressive rollout. The results indicate that the proposed finite element inspired learned simulator can support manufacturability oriented field prediction and efficient design space exploration in large deformation sheet material forming.

有限元仿真图神经网络钣金成形制造优化

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