The quality of mesh generation has long been considered a vital aspect in providing engineers with reliable simulation results throughout the history of the Finite Element Method (FEM). The element extraction method, which is currently the most robust method, is used in business software. However, in order to speed up extraction, the approach is done by finding the next element that optimizes a target function, which can result in local mesh of bad quality after many time steps. We provide TreeMesh, a method that uses this method in conjunction with reinforcement learning (also possible with supervised learning) and a novel Monte-Carlo tree search (MCTS) (Coulom(2006), Kocsis and Szepesv\'ari(2006), Browne et~al.(2012)). The algorithm is based on a previously proposed approach (Pan et~al.(2021)). After making many improvements on DRL (algorithm, state-action-reward setting) and adding a MCTS, it outperforms the former work on the same boundary. Furthermore, using tree search, our program reveals much preponderance on seed-density-changing boundaries, which is common on thin-film materials.

翻译：网格生成质量长期以来被视为有限元法（FEM）中为工程师提供可靠仿真结果的关键要素。当前最稳健的单元提取方法已被应用于商业软件中，然而为加速提取过程，该方法通过寻找优化目标函数的下一单元来实现，这可能导致长时间步后产生局部劣质网格。我们提出TreeMesh方法，该方法将该技术结合强化学习（亦可采用监督学习）与新型蒙特卡洛树搜索（MCTS）（Coulom(2006)、Kocsis和Szepesvári(2006)、Browne等(2012)）进行应用。该算法基于先前提出的方法（Pan等(2021)），在对深度强化学习（算法、状态-动作-奖励设置）进行多项改进并引入MCTS后，其在相同边界上的表现优于先前工作。此外，采用树搜索后，我们的程序在种子密度变化的边界（常见于薄膜材料）上展现出显著优势。