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:Translated abstract:
高质量的网格生成是准确的有限元分析的基础。由于广阔的内部顶点搜索空间和复杂的初始边界,对于复杂领域的网格生成需要大量手动处理,并长期被认为是整个建模和分析过程中最具挑战性和耗时的瓶颈。本文提出了一种新的计算框架,名为“SRL辅助AFM”,通过将前进法与选择参考顶点的神经网络结合,并使用“策略网络”更新前沿边界,来网格化平面几何。这些深度神经网络是通过独特的流程进行训练的,包括结合监督学习和强化学习以迭代提高网格质量的阶段。首先,我们通过在正方形区域中随机抽取点并依次连接它们来生成不同的初始边界。这些边界用于获得输入网格和提取监督学习模块中的训练数据集。然后,我们使用特殊需求的奖励函数(如改进网格质量和控制异常点数量和分布)迭代提高强化学习模型的性能。我们提出的监督学习神经网络在预测商业软件时实现了高达98%的准确度。最后,强化学习神经网络可自动生成具有锐利特征和边界层的复杂平面域的高质量四边形网格。