Chunye Gong

Xinhai Chen, Jie Liu, Junjun Yan et al.

Mesh generation remains a key technology in many areas where numerical simulations are required. As numerical algorithms become more efficient and computers become more powerful, the percentage of time devoted to mesh generation becomes higher. In this paper, we present an improved structured mesh generation method. The method formulates the meshing problem as a global optimization problem related to a physics-informed neural network. The mesh is obtained by intelligently solving the physical boundary-constrained partial differential equations. To improve the prediction accuracy of the neural network, we also introduce a novel auxiliary line strategy and an efficient network model during meshing. The strategy first employs a priori auxiliary lines to provide ground truth data and then uses these data to construct a loss term to better constrain the convergence of the subsequent training. The experimental results indicate that the proposed method is effective and robust. It can accurately approximate the mapping (transformation) from the computational domain to the physical domain and enable fast high-quality structured mesh generation.

Zhichao Wang, Xinhai Chen, Chunye Gong et al.

Mesh smoothing methods can enhance mesh quality by eliminating distorted elements, leading to improved convergence in simulations. To balance the efficiency and robustness of traditional mesh smoothing process, previous approaches have employed supervised learning and reinforcement learning to train intelligent smoothing models. However, these methods heavily rely on labeled dataset or prior knowledge to guide the models' learning. Furthermore, their limited capacity to enhance mesh connectivity often restricts the effectiveness of smoothing. In this paper, we first systematically analyze the learning mechanisms of recent intelligent smoothing methods and propose a prior-free reinforcement learning model for intelligent mesh smoothing. Our proposed model integrates graph neural networks with reinforcement learning to implement an intelligent node smoothing agent and introduces, for the first time, a mesh connectivity improvement agent. We formalize mesh optimization as a Markov Decision Process and successfully train both agents using Twin Delayed Deep Deterministic Policy Gradient and Double Dueling Deep Q-Network in the absence of any prior data or knowledge. We verified the proposed model on both 2D and 3D meshes. Experimental results demonstrate that our model achieves feature-preserving smoothing on complex 3D surface meshes. It also achieves state-of-the-art results among intelligent smoothing methods on 2D meshes and is 7.16 times faster than traditional optimization-based smoothing methods. Moreover, the connectivity improvement agent can effectively enhance the quality distribution of the mesh.