用图神经网络简化网格，大幅提升网格生成效率
Generating Sizing Fields for Mesh Generation via GCN-based Simplification of Adaptive Background Grids
- 将网格简化转化为边的评分回归问题，用GCN预测最优删边
- 简化后元素减少74%-94%，查询时间降低35%-88%
- 适合需要高效网格生成的工程仿真场景
定义在三角形背景网格上的尺寸场对非结构化网格生成的质量与效率至关重要。然而，构建几何一致、计算轻量且无条纹等伪影的最优背景网格仍是一项重大挑战。本文提出一种基于图卷积网络（GCN）的自适应背景网格简化（ABGS）框架。将网格简化任务重构为边评分回归问题，训练GCN模型以高效预测最优边合并候选。模型通过自定义损失函数，综合考虑几何保真度与尺寸场精度。该数据驱动方法替代了耗时的程序化评估，显著加速简化过程。实验表明，本框架在多种复杂工程模型上均具有效性：相比初始密集网格，简化后的背景网格元素减少74%-94%，尺寸场查询时间降低35%-88%。
原文摘要 · Abstract (English)
The sizing field defined on a triangular background grid is pivotal for controlling the quality and efficiency of unstructured mesh generation. However, creating an optimal background grid that is geometrically conforming, computationally lightweight, and free from artifacts like banding is a significant challenge. This paper introduces a novel, adaptive background grid simplification (ABGS) framework based on a Graph Convolutional Network (GCN). We reformulate the grid simplification task as an edge score regression problem and train a GCN model to efficiently predict optimal edge collapse candidates. The model is guided by a custom loss function that holistically considers both geometric fidelity and sizing field accuracy. This data-driven approach replaces a costly procedural evaluation, accelerating the simplification process. Experimental results demonstrate the effectiveness of our framework across diverse and complex engineering models. Compared to the initial dense grids, our simplified background grids achieve an element reduction of 74%-94%, leading to a 35%-88% decrease in sizing field query times.
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