# MeshingNet: A New Mesh Generation Method based on Deep Learning

arXiv: https://arxiv.org/abs/2004.07016 · HTML: https://mlsanity.com/paper/2004.07016/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Apr 2020.

## Built on by (most cited first, 30 of 30)

- [Deep Generative Models in Engineering Design: A Review](https://mlsanity.com/paper/2110.10863/) (2021)
- [Human Trajectory Prediction via Neural Social Physics](https://mlsanity.com/paper/2207.10435/) (2022)
- [Blending Neural Operators and Relaxation Methods in PDE Numerical Solvers](https://mlsanity.com/paper/2208.13273/) (2022)
- [Reinforcement Learning for Adaptive Mesh Refinement](https://mlsanity.com/paper/2103.01342/) (2021)
- [Physics-Guided, Physics-Informed, and Physics-Encoded Neural Networks in Scientific Computing](https://mlsanity.com/paper/2211.07377/) (2022)
- [Deep Learning in Deterministic Computational Mechanics](https://mlsanity.com/paper/2309.15421/) (2023)
- [Reinforcement learning for automatic quadrilateral mesh generation: a soft actor-critic approach](https://mlsanity.com/paper/2203.11203/) (2022)
- [Swarm Reinforcement Learning For Adaptive Mesh Refinement](https://mlsanity.com/paper/2304.00818/) (2023)
- [M2N: Mesh Movement Networks for PDE Solvers](https://mlsanity.com/paper/2204.11188/) (2022)
- [Learning robust marking policies for adaptive mesh refinement](https://mlsanity.com/paper/2207.06339/) (2022)
- [What's the Situation with Intelligent Mesh Generation: A Survey and Perspectives](https://mlsanity.com/paper/2211.06009/) (2022)
- [Feature Engineering with Regularity Structures](https://mlsanity.com/paper/2108.05879/) (2021)
- [E2N: Error Estimation Networks for Goal-Oriented Mesh Adaptation](https://mlsanity.com/paper/2207.11233/) (2022)
- [Human Trajectory Forecasting with Explainable Behavioral Uncertainty](https://mlsanity.com/paper/2307.01817/) (2023)
- [Quasi-optimal hp-finite element refinements towards singularities via deep neural network prediction](https://mlsanity.com/paper/2209.05844/) (2022)
- [Towards Universal Mesh Movement Networks](https://mlsanity.com/paper/2407.00382/) (2024)
- [AMBER: Adaptive Mesh Generation by Iterative Mesh Resolution Prediction](https://mlsanity.com/paper/2505.23663/) (2025)
- [A Deep Double Ritz Method (D2RM) for solving Partial Differential Equations using Neural Networks](https://mlsanity.com/paper/2211.03627/) (2022)
- [3DMeshNet: A Three-Dimensional Differential Neural Network for Structured Mesh Generation](https://mlsanity.com/paper/2407.01560/) (2024)
- [Reinforcement Learning for Block Decomposition of CAD Models](https://mlsanity.com/paper/2302.11066/) (2023)
- [Bayesian Differentiable Physics for Cloth Digitalization](https://mlsanity.com/paper/2402.17664/) (2024)
- [UGM2N: An Unsupervised and Generalizable Mesh Movement Network via M-Uniform Loss](https://mlsanity.com/paper/2508.08615/) (2025)
- [Proposing an intelligent mesh smoothing method with graph neural networks](https://mlsanity.com/paper/2311.12815/) (2023)
- [Polyhedral Complex Derivation from Piecewise Trilinear Networks](https://mlsanity.com/paper/2402.10403/) (2024)
- [MeshONet: A Generalizable and Efficient Operator Learning Method for Structured Mesh Generation](https://mlsanity.com/paper/2501.11937/) (2025)
- [A Mesh Is Worth 512 Numbers: Spectral-domain Diffusion Modeling for High-dimension Shape Generation](https://mlsanity.com/paper/2503.06485/) (2025)
- [Learning Extremely High Density Crowds as Active Matters](https://mlsanity.com/paper/2503.12168/) (2025)
- [Dmsh: A Multi-Agent Reinforcement Learning Framework for All-Quad Mesh Generation](https://mlsanity.com/paper/2606.10601/) (2026)
- [Paradigm Shift Through the Integration of Physical Methodology and Data Science](https://mlsanity.com/paper/2110.01408/) (2021)
- [Efficient temporal prediction of compressible flows in irregular domains using Fourier neural operators](https://mlsanity.com/paper/2601.01922/) (2026)

## Abstract (arXiv)

We introduce a novel approach to automatic unstructured mesh generation using machine learning to predict an optimal finite element mesh for a previously unseen problem. The framework that we have developed is based around training an artificial neural network (ANN) to guide standard mesh generation software, based upon a prediction of the required local mesh density throughout the domain. We describe the training regime that is proposed, based upon the use of a posteriori error estimation, and discuss the topologies of the ANNs that we have considered. We then illustrate performance using two standard test problems, a single elliptic partial differential equation (PDE) and a system of PDEs associated with linear elasticity. We demonstrate the effective generation of high quality meshes for arbitrary polygonal geometries and a range of material parameters, using a variety of user-selected error norms.