arXiv:2505.23663cs.LGcs.CG2025-05NeurIPS被引 4

用AI自动生成高精度有限元网格,省去专家手动调参。

AMBER: Adaptive Mesh Generation by Iterative Mesh Resolution Prediction

  • 通过图神经网络预测网格尺寸分布,迭代生成优化网格。
  • 在2D/3D物理与工业场景中,精度高于现有多种AI方法。
  • 无需人工设计,可泛化到未见几何结构,适合工程仿真场景。

使用有限元法(FEM)模拟复杂物理系统时,计算成本和精度随网格分辨率提升而增加。自适应网格通过在关键区域细化网格提高效率,但通常依赖特定任务的启发式规则或人工专家设计。本文提出基于专家重构的自适应网格生成方法(AMBER),从粗网格开始,利用监督学习迭代预测尺寸场(即几何到局部单元大小的映射函数),并借助现成网格生成器构建新中间网格。该过程基于分层图神经网络实现,并在训练中通过自动将专家标签投影到AMBER生成数据上进行数据增强。我们在2D和3D数据集上评估了AMBER,涵盖经典物理问题、机械部件及真实工业设计,均配有专家标注网格。AMBER能泛化至未见几何结构,在多项指标上持续优于多个近期基线方法,包括基于图神经网络、卷积神经网络及强化学习的方法。

原文摘要 · Abstract (English)

The cost and accuracy of simulating complex physical systems using the Finite Element Method (FEM) scales with the resolution of the underlying mesh. Adaptive meshes improve computational efficiency by refining resolution in critical regions, but typically require task-specific heuristics or cumbersome manual design by a human expert. We propose Adaptive Meshing By Expert Reconstruction (AMBER), a supervised learning approach to mesh adaptation. Starting from a coarse mesh, AMBER iteratively predicts the sizing field, i.e., a function mapping from the geometry to the local element size of the target mesh, and uses this prediction to produce a new intermediate mesh using an out-of-the-box mesh generator. This process is enabled through a hierarchical graph neural network, and relies on data augmentation by automatically projecting expert labels onto AMBER-generated data during training. We evaluate AMBER on 2D and 3D datasets, including classical physics problems, mechanical components, and real-world industrial designs with human expert meshes. AMBER generalizes to unseen geometries and consistently outperforms multiple recent baselines, including ones using Graph and Convolutional Neural Networks, and Reinforcement Learning-based approaches.

网格生成有限元图神经网络自动化

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