Generate plane quad mesh with neural networks and tree search
This work addresses mesh generation for engineers using FEM, offering incremental improvements over prior methods.
The paper tackles the problem of generating high-quality plane quad meshes for finite element simulations by introducing TreeMesh, which combines reinforcement learning with Monte-Carlo tree search to improve upon existing element extraction methods, resulting in outperformance on standard boundaries and better handling of seed-density-changing boundaries common in thin-film materials.
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 Szepesvári(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.