High-quality mesh generation is the foundation of accurate finite element analysis. Due to the vast interior vertices search space and complex initial boundaries, mesh generation for complicated domains requires substantial manual processing and has long been considered the most challenging and time-consuming bottleneck of the entire modeling and analysis process. In this paper, we present a novel computational framework named ``SRL-assisted AFM" for meshing planar geometries by combining the advancing front method with neural networks that select reference vertices and update the front boundary using ``policy networks." These deep neural networks are trained using a unique pipeline that combines supervised learning with reinforcement learning to iteratively improve mesh quality. First, we generate different initial boundaries by randomly sampling points in a square domain and connecting them sequentially. These boundaries are used for obtaining input meshes and extracting training datasets in the supervised learning module. We then iteratively improve the reinforcement learning model performance with reward functions designed for special requirements, such as improving the mesh quality and controlling the number and distribution of extraordinary points. Our proposed supervised learning neural networks achieve an accuracy higher than 98% on predicting commercial software. The final reinforcement learning neural networks automatically generate high-quality quadrilateral meshes for complex planar domains with sharp features and boundary layers.

翻译：高质量网格生成是精确有限元分析的基础。由于内部顶点搜索空间庞大且初始边界复杂，复杂区域的网格生成需要大量人工处理，并长期被视为整个建模与分析过程中最具挑战性且最耗时的瓶颈。本文提出一种名为"SRL辅助AFM"的新型计算框架，通过将波前法与神经网络相结合，利用"策略网络"选择参考顶点并更新前沿边界。这些深度神经网络采用结合监督学习和强化学习的独特流水线进行训练，以迭代提升网格质量。首先，通过在正方形区域内随机采样点并依次连接生成不同初始边界，利用这些边界获取输入网格并在监督学习模块中提取训练数据集。随后，我们通过针对特殊需求（如提升网格质量、控制奇异点的数量与分布）设计的奖励函数迭代优化强化学习模型性能。所提出的监督学习神经网络对商业软件网格的预测准确率超过98%。最终强化学习神经网络可自动为包含尖角特征和边界层的复杂平面域生成高质量四边形网格。