arXiv：cs.AI· Manuel Ricardo Guevara Garban, Yves Chemisky, \'Etienne Pruli\`ere, Micha\"el Cl\'ement·· 16 小时前
P-DivGNN：用物理信息图神经网络重建有限应变超弹性下的局部应力场
Physics-Informed Graph Neural Networks to Reconstruct Local Fields Considering Finite Strain Hyperelasticity
AI 导读
研究者提出物理信息机器学习框架 P-DivGNN，将周期性微结构表示为图并结合消息传递图神经网络，在给定宏观平均应力值的情况下重建微观尺度局部应力场。模型在训练中引入物理约束以保证局部应力场平衡状态，并用周期性图表示施加周期性边界条件。在线性与非线性超弹性响应下评估显示，非线性超弹性情形相比有限元模拟取得显著计算加速。
正文
Abstract:We propose a physics-informed machine learning framework called P-DivGNN to reconstruct local stress fields at the micro-scale, in the context of multi-scale simulation given a periodic micro-structure mesh and mean, macro-scale, stress values. This method is based in representing a periodic micro-structure as a graph, combined with a message passing graph neural network. We are able to retrieve local stress field distributions, providing average stress values produced by a mean field reduced order model (ROM) or Finite Element (FE) simulation at the macro-scale. The prediction of local stress fields are of utmost importance considering fracture analysis or the definition of local fatigue criteria. Our model incorporates physical constraints during training to constraint local stress field equilibrium state and employs a periodic graph representation to enforce periodic boundary conditions. The benefits of the proposed physics-informed GNN are evaluated considering linear and non linear hyperelastic responses applied to varying geometries. In the non-linear hyperelastic case, the proposed method achieves significant computational speed-ups compared to FE simulation, making it particularly attractive for large-scale applications.
| Subjects: | Machine Learning (cs.LG); Materials Science (cond-mat.mtrl-sci); Artificial Intelligence (cs.AI); Computational Physics (physics.comp-ph) |
| Cite as: | arXiv:2507.05291 [cs.LG] |
| (or arXiv:2507.05291v2 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2507.05291 arXiv-issued DOI via DataCite |
Submission history
From: Manuel Ricardo Guevara Garban [view email]
[v1]
Sat, 5 Jul 2025 13:11:31 UTC (12,653 KB)
[v2]
Tue, 13 Oct 2026 11:26:25 UTC (13,000 KB)
来源：arXiv：cs.AI · arxiv.org