# An Improved Structured Mesh Generation Method Based on Physics-informed Neural Networks

arXiv: https://arxiv.org/abs/2210.09546 · HTML: https://mlsanity.com/paper/2210.09546/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 40 references that are in the map.
- First posted on arXiv 18 Oct 2022.

## Builds on (most cited first, 7 of 7)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Physics-informed neural networks (PINNs) for fluid mechanics: A review](https://mlsanity.com/paper/2105.09506/) (2021)
- [hp-VPINNs: Variational Physics-Informed Neural Networks With Domain Decomposition](https://mlsanity.com/paper/2003.05385/) (2020)
- [Understanding and mitigating gradient pathologies in physics-informed neural networks](https://mlsanity.com/paper/2001.04536/) (2020)
- [An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications](https://mlsanity.com/paper/1908.10407/) (2019)
- [CFDNet: a deep learning-based accelerator for fluid simulations](https://mlsanity.com/paper/2005.04485/) (2020)
- [Application of Convolutional Neural Network to Predict Airfoil Lift Coefficient](https://mlsanity.com/paper/1712.10082/) (2017)

## Built on by (most cited first, 4 of 4)

- [3DMeshNet: A Three-Dimensional Differential Neural Network for Structured Mesh Generation](https://mlsanity.com/paper/2407.01560/) (2024)
- [Auxiliary-Tasks Learning for Physics-Informed Neural Network-Based Partial Differential Equations Solving](https://mlsanity.com/paper/2307.06167/) (2023)
- [MeshONet: A Generalizable and Efficient Operator Learning Method for Structured Mesh Generation](https://mlsanity.com/paper/2501.11937/) (2025)
- [Loop2Net: Data-Driven Generation and Optimization of Airfoil CFD Meshes from Sparse Boundary Coordinates](https://mlsanity.com/paper/2507.01057/) (2025)

## Abstract (arXiv)

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.