Generate plane quad mesh with neural networks and tree search

TL;DR

This paper introduces TreeMesh, a novel mesh generation method combining element extraction, reinforcement learning, and Monte-Carlo tree search to improve mesh quality and efficiency, especially for complex boundaries.

Contribution

The paper presents TreeMesh, integrating MCTS with reinforcement learning to enhance mesh generation quality and speed over traditional methods.

Findings

Outperforms previous approaches on the same boundary.

Shows significant advantages on seed-density-changing boundaries.

Improves mesh quality and computational efficiency.

Abstract

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.