An Improved Structured Mesh Generation Method Based on Physics-informed Neural Networks
This work addresses mesh generation, a bottleneck in numerical simulations, by proposing an incremental improvement to existing methods.
The paper tackles the problem of structured mesh generation for numerical simulations by formulating it as a global optimization problem using physics-informed neural networks, with results showing effective and robust performance in accurately approximating domain mappings and enabling fast high-quality mesh generation.
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.