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.

通过将网格生成相关的微分方程嵌入神经网络的损失函数中，我们提出了一种新的方法，3DMeshNet，用于三维结构化网格的生成。该方法以几何点为输入，学习参数化和计算域之间的潜在映射，并通过前向神经预测高效地输出具有用户定义的四边形 / 六面体单元数的三维结构化网格。实验表明，3DMeshNet 稳健且快速，并且与传统的网格划分方法相比，产生优越的网格，并且相对于其他基于神经网络的方法减少了高达 85% 的训练时间，将网格生成开销降低了 4 至 8 倍。

3DMeshNet：一种用于结构化网格生成的三维差分神经网络

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

With the development of computational fluid dynamics, the requirements for
the fluid simulation accuracy in industrial applications have also increased.
The quality of the generated mesh directly affects the simulation accuracy.
However, previous mesh quality metrics and models cannot evaluate meshes
comprehensively and objectively. To this end, we propose MQENet, a structured
mesh quality evaluation neural network based on dynamic graph attention. MQENet
treats the mesh evaluation task as a graph classification task for classifying
the quality of the input structured mesh. To make graphs generated from
structured meshes more informative, MQENet introduces two novel structured mesh
preprocessing algorithms. These two algorithms can also improve the conversion
efficiency of structured mesh data. Experimental results on the benchmark
structured mesh dataset NACA-Market show the effectiveness of MQENet in the
mesh quality evaluation task.

通过提出 MQENet 这种基于动态图注意力的结构化网格质量评估神经网络，可以更全面客观地评估工业应用中的结构化网格质量，从而提高流体模拟精度。