# 3DMeshNet: A Three-Dimensional Differential Neural Network for Structured Mesh Generation

arXiv: https://arxiv.org/abs/2407.01560 · HTML: https://mlsanity.com/paper/2407.01560/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 40 references that are in the map.
- First posted on arXiv 7 May 2024.

## Builds on (most cited first, 11 of 11)

- [Multi-Task Learning Using Uncertainty to Weigh Losses for Scene Geometry and Semantics](https://mlsanity.com/paper/1705.07115/) (2017)
- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [CAN-PINN: A Fast Physics-Informed Neural Network Based on Coupled-Automatic-Numerical Differentiation Method](https://mlsanity.com/paper/2110.15832/) (2021)
- [CFDNet: a deep learning-based accelerator for fluid simulations](https://mlsanity.com/paper/2005.04485/) (2020)
- [MeshingNet: A New Mesh Generation Method based on Deep Learning](https://mlsanity.com/paper/2004.07016/) (2020)
- [Application of Convolutional Neural Network to Predict Airfoil Lift Coefficient](https://mlsanity.com/paper/1712.10082/) (2017)
- [Machine Learning-Based Optimal Mesh Generation in Computational Fluid Dynamics](https://mlsanity.com/paper/2102.12923/) (2021)
- [An Improved Structured Mesh Generation Method Based on Physics-informed Neural Networks](https://mlsanity.com/paper/2210.09546/) (2022)
- [Auxiliary-Tasks Learning for Physics-Informed Neural Network-Based Partial Differential Equations Solving](https://mlsanity.com/paper/2307.06167/) (2023)
- [MQENet: A Mesh Quality Evaluation Neural Network Based on Dynamic Graph Attention](https://mlsanity.com/paper/2309.01067/) (2023)

## Built on by (most cited first, 3 of 3)

- [LLM4Fluid: Large Language Models as Generalizable Neural Solvers for Fluid Dynamics](https://mlsanity.com/paper/2601.21681/) (2026)
- [GS-DMSR: Dynamic Sensitive Multi-scale Manifold Enhancement for Accelerated High-Quality 3D Gaussian Splatting](https://mlsanity.com/paper/2601.05584/) (2026)
- [Q-MAGIC: Quad-only Mesh Autoregressive Generation via Singularity-Aware Circular Relative Offset Tokenization](https://mlsanity.com/paper/2610.19777/) (2026)

## Abstract (arXiv)

Mesh generation is a crucial step in numerical simulations, significantly impacting simulation accuracy and efficiency. However, generating meshes remains time-consuming and requires expensive computational resources. In this paper, we propose a novel method, 3DMeshNet, for three-dimensional structured mesh generation. The method embeds the meshing-related differential equations into the loss function of neural networks, formulating the meshing task as an unsupervised optimization problem. It takes geometric points as input to learn the potential mapping between parametric and computational domains. After suitable offline training, 3DMeshNet can efficiently output a three-dimensional structured mesh with a user-defined number of quadrilateral/hexahedral cells through the feed-forward neural prediction. To enhance training stability and accelerate convergence, we integrate loss function reweighting through weight adjustments and gradient projection alongside applying finite difference methods to streamline derivative computations in the loss. Experiments on different cases show that 3DMeshNet is robust and fast. It outperforms neural network-based methods and yields superior meshes compared to traditional mesh partitioning methods. 3DMeshNet significantly reduces training times by up to 85% compared to other neural network-based approaches and lowers meshing overhead by 4 to 8 times relative to traditional meshing methods.