arXiv：cs.LG· Yingxue Zhao, Haoran Li, Haosu Zhou, Tobias Pfaff, Nan Li·· 4 小时前
CAtt-BiGNN：受有限元启发的二分图学习模拟器，用于大变形板料成形的可制造性评估
A finite-element-inspired bipartite graph learned simulator for manufacturability assessment in large-deformation sheet forming
AI 导读
研究者提出 CAtt-BiGNN，一种基于交叉注意力的二分图神经网络，将网格节点与单元建模为不同图实体，在各自原生域上耦合预测节点位移增量与单元减薄。该模型无需施加平衡或本构约束，其大规模版本 CAtt-BiUGNN 通过节点与单元的独立降采样和上采样增强长程传播。
正文
Abstract: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.
| Subjects: | Computational Engineering, Finance, and Science (cs.CE); Machine Learning (cs.LG) |
| Cite as: | arXiv:2605.22845 [cs.CE] |
| (or arXiv:2605.22845v3 [cs.CE] for this version) | |
| https://doi.org/10.48550/arXiv.2605.22845 arXiv-issued DOI via DataCite |
Submission history
From: Nan Li [view email]
[v1]
Thu, 14 May 2026 17:12:44 UTC (8,108 KB)
[v2]
Tue, 16 Jun 2026 23:15:06 UTC (49,313 KB)
[v3]
Tue, 13 Oct 2026 23:27:46 UTC (17,268 KB)
来源：arXiv：cs.LG · arxiv.org