Automatic generation of high-quality meshes is a base of CAD/CAE systems. The element extraction is a major mesh generation method for its capabilities to generate high-quality meshes around the domain boundary and to control local mesh densities. However, its widespread applications have been inhibited by the difficulties in generating satisfactory meshes in the interior of a domain or even in generating a complete mesh. The element extraction method's primary challenge is to define element extraction rules for achieving high-quality meshes in both the boundary and the interior of a geometric domain with complex shapes. This paper presents a self-learning element extraction system, FreeMesh-S, that can automatically acquire robust and high-quality element extraction rules. Two central components enable the FreeMesh-S: (1) three primitive structures of element extraction rules, which are constructed according to boundary patterns of any geometric boundary shapes; (2) a novel self-learning schema, which is used to automatically define and refine the relationships between the parameters included in the element extraction rules, by combining an Advantage Actor-Critic (A2C) reinforcement learning network and a Feedforward Neural Network (FNN). The A2C network learns the mesh generation process through random mesh element extraction actions using element quality as a reward signal and produces high-quality elements over time. The FNN takes the mesh generated from the A2C as samples to train itself for the fast generation of high-quality elements. FreeMesh-S is demonstrated by its application to two-dimensional quad mesh generation. The meshing performance of FreeMesh-S is compared with three existing popular approaches on ten pre-defined domain boundaries. The experimental results show that even with much less domain knowledge required to develop the algorithm, FreeMesh-S outperforms those three approaches in essential indices. FreeMesh-S significantly reduces the time and expertise needed to create high-quality mesh generation algorithms.

中文翻译：

---

基于强化学习的自学习有限元提取系统

自动生成高质量网格是 CAD/CAE 系统的基础。单元提取是一种主要的网格生成方法，因为它能够在域边界周围生成高质量的网格并控制局部网格密度。然而，由于难以在域内部生成令人满意的网格，甚至难以生成完整的网格，它的广泛应用受到了阻碍。单元提取方法的主要挑战是定义单元提取规则，以在具有复杂形状的几何域的边界和内部实现高质量的网格。本文提出了一种自学习的元素提取系统FreeMesh-S，它可以自动获取鲁棒和高质量的元素提取规则。两个核心组件支持 FreeMesh-S：(1) 元素提取规则的三个原始结构，根据任意几何边界形状的边界模式构建；(2) 一种新颖的自学习模式，用于通过结合 Advantage Actor-Critic (A2C) 强化学习网络和前馈神经网络 (FNN) 来自动定义和细化元素提取规则中包含的参数之间的关系）。A2C 网络通过使用元素质量作为奖励信号的随机网格元素提取动作来学习网格生成过程，并随着时间的推移产生高质量的元素。FNN 将 A2C 生成的网格作为样本来训练自己以快速生成高质量元素。FreeMesh-S 通过其在二维四边形网格生成中的应用得到了展示。将 FreeMesh-S 的网格划分性能与十个预定义域边界上的三种现有流行方法进行比较。实验结果表明，即使开发算法所需的领域知识少得多，FreeMesh-S 在基本指标上也优于这三种方法。FreeMesh-S 显着减少了创建高质量网格生成算法所需的时间和专业知识。