We describe a new algorithm for the generation of high quality tetrahedral meshes using artificial neural networks. The goal is to generate close-to-optimal meshes in the sense that the error in the computed finite element (FE) solution (for a target system of partial differential equations (PDEs)) is as small as it could be for a prescribed number of nodes or elements in the mesh. In this paper we illustrate and investigate our proposed approach by considering the equations of linear elasticity, solved on a variety of three-dimensional geometries. This class of PDE is selected due to its equivalence to an energy minimization problem, which therefore allows a quantitative measure of the relative accuracy of different meshes (by comparing the energy associated with the respective FE solutions on these meshes). Once the algorithm has been introduced it is evaluated on a variety of test problems, each with its own distinctive features and geometric constraints, in order to demonstrate its effectiveness and computational efficiency.

我们描述了一种使用人工神经网络生成高质量四面体网格的新算法。目标是在某种意义上生成接近最佳的网格，即计算的有限元（FE）解决方案中的误差（对于偏微分方程（PDE）的目标系统）应尽可能小。网格中节点或元素的数量。在本文中，我们通过考虑在各种三维几何形状上求解的线性弹性方程，来说明和研究我们提出的方法。选择此类PDE是因为它等效于能量最小化问题，因此可以定量测量不同网格的相对精度（通过比较与这些网格上的各个FE解相关的能量）。