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

2025-03-02

AI Summary

Generating high-quality structured quadrilateral meshes remains time-consuming and challenging to balance efficiency with mesh quality. To address this, we propose an end-to-end unsupervised method based on physics-informed neural networks (PINNs), which takes boundary curves as input and learns the mapping from a computational domain to the physical domain via an attention mechanism. Our key innovation lies in embedding the Navier–Lamé equation directly into the PINN loss function to enforce physical consistency of elastic deformation—enabling fully unsupervised training without labeled data, pre-existing meshes, or manual intervention. Experiments demonstrate that our generated meshes significantly outperform state-of-the-art algebraic and PDE-based methods across critical quality metrics, including angle preservation, orthogonality, and Jacobian determinant distribution, while achieving both high accuracy and computational efficiency.

Technology Category

• Computer Vision: Low Level & Physics-based Vision
• Natural Language Processing: Generation
• Machine Learning: Learning with Manifolds

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Web data generation and simulation
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications

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-Lam'e 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.

Problem

• Efficient structured mesh generation for numerical simulations
• Ensuring high-quality meshes using physics-informed neural networks
• Unsupervised training without prior datasets for mesh generation

Innovation

• Physics-informed neural network for mesh generation
• Unsupervised training without prior datasets
• Incorporates Navier-Lamé equation in loss function