Unstructured surface mesh smoothing method based on deep reinforcement learning

In numerical simulations such as computational fluid dynamics simulations or finite element analyses, mesh quality affects simulation accuracy directly and significantly. Smoothing is one of the most widely adopted methods to improve unstructured mesh quality in mesh generation practices. Compared with the optimization-based smoothing method, heuristic smoothing methods are efficient but yield lower mesh quality. The balance between smoothing efficiency and mesh quality has been pursued in previous studies. In this paper, we propose a new smoothing method that combines the advantages of the heuristic Laplacian method and the optimization-based method based on the deep reinforcement learning method under the Deep Deterministic Policy Gradient framework. Within the framework, the actor artificial neural network predicts the optimal position of each interior free node with its surrounding ring nodes. At the same time, a critic-network is established and takes the mesh quality as input and outputs the reward of the action taken by the actor-network. Training of the networks will maximize the cumulative long-term reward, which ends up maximizing the mesh quality. Training and validation of the proposed method are presented both on 2-dimensional triangular meshes and 3-dimensional surface meshes, which demonstrates the efficiency and mesh quality of the proposed method. Finally, numerical simulations on perturbed meshes and smoothed meshes are carried out and compared which prove the influence of mesh quality on the simulation accuracy.