PINN-MG: A physics-informed neural network for mesh generation

TL;DR

This paper addresses the challenge of efficient and high-quality structured mesh generation by proposing PINN-MG, a physics-informed neural network that learns the mapping from a regular computational domain to a target physical domain using boundary curves as input. It embeds the Navier-Lamé elasticity equations into the loss to enforce physical deformation, and employs boundary-condition processing with SVR and an attention-based network with input augmentation to predict mesh node displacements in the physical domain. The approach is unsupervised, requiring no prior mesh datasets, and demonstrates superior structured quad meshes relative to algebraic methods while maintaining competitive generation times. The work offers a scalable, physics-consistent alternative for industrial simulations and lays groundwork for extending PINN-based mesh generation to other topologies.

Abstract

In numerical simulation, structured mesh generation often requires a lot of time and manpower investment. The general scheme for structured quad mesh generation is to find a mapping between the computational domain and the physical domain. This mapping can be obtained by solving partial differential equations. However, existing structured mesh generation methods are difficult to ensure both efficiency and mesh quality. In this paper, we propose a structured mesh generation method based on physics-informed neural network, PINN-MG. It takes boundary curves as input and then utilizes an attention network to capture the potential mapping between computational and physical domains, generating structured meshes for the input physical domain. PINN-MG introduces the Navier-Lamé equation in linear elastic as a partial differential equation term in the loss function, ensuring that the neural network conforms to the law of elastic body deformation when optimizing the loss value. The training process of PINN-MG is completely unsupervised and does not require any prior knowledge or datasets, which greatly reduces the previous workload of producing structured mesh datasets. Experimental results show that PINN-MG can generate higher quality structured quad meshes than other methods, and has the advantages of traditional algebraic methods and differential methods.

Figures (12)

• Figure 1: An example of a linear elasticity problem.
• Figure 2: The Mapping relationship between computational domain mesh and physical domain mesh.
• Figure 3: The architecture of the proposed PINN-MG.
• Figure 4: Overall loss of PINN-MG on the structured mesh generation task.
• Figure 5: Results of different structured mesh generation methods on model3.