Universal mesh generation method based on physics-informed neural network

doi:10.11996/JG.j.2095-302X.2025050990

Abstract

Abstract:

Structured mesh generation in numerical simulation often requires a lot of time and manpower. Traditionally, the process relies on establishing a mapping between the computational domain and the physical domain, which is typically obtained by solving partial differential equations. However, existing structured mesh generation methods struggle to simultaneously achieve both high efficiency and superior mesh quality. To address this issue, we propose a universal mesh generation model based on physics-informed neural network (UMG-PINN). This model formulates mesh generation task as a mesh deformation problem from the computational domain to the physical domain. By taking the boundary curve as input and leveraging an attention network, UMG-PINN captures the potential mapping between the computational and physical domains, thereby generating high-quality structured mesh. To enforce physical constraints, the model incorporates the Navier-Lamé equation from linear elasticity into the loss function, ensuring that the neural network conforms to the principles of elastic body deformation during optimization. A key advantage of UMG-PINN is its fully self-supervised training process, which eliminates the need for prior knowledge or pre-existing datasets, greatly reducing the effort required for structured mesh dataset construction. Experimental results show that UMG-PINN outperforms traditional transfinite interpolation methods by generating higher quality structured meshes. In addition, UMG-PINN can also be extended to unstructured mesh generation under the constraints of physical information.

Key words: mesh generation, physics-informed neural network, Navier-Lamé equation, self-supervised learning

CLC Number:

TP183

ZHANG Haoxuan, LI Haisheng, WANG Min, LI Nan. Universal mesh generation method based on physics-informed neural network[J]. Journal of Graphics, 2025, 46(5): 990-997.

Figures/Tables 12

Fig. 1 The overall network architecture of UMG-PINN

Fig. 2 Results of different structured mesh generation methods on model3 ((a) TFI; (b) MGNet+hyperbola equation; (c) MGNet+poisson equation; (d) UMGPINN)

Fig. 3 Results of different structured mesh generation methods on model4 ((a) MGNet+hyperbola equation;(b) MGNet+poisson equation; (c) UMGPINN)

Fig. 4 Results of different structured mesh generation methods on model5 ((a) TFI; (b) MGNet+hyperbola equation; (c) MGNet+poisson equation; (d) UMGPINN)

Fig. 5 Results of 3D structured mesh generation on different models ((a) Model 1; (b) Model 2; (c) Model 3)

Table 1 A comparison of average min/max included angle for different models of structured meshes/(°)

模型	TFI	MGNet^[31]+泊松方程	MGNet^[31]+双曲线方程	Ours
模型1	83.66/96.40	85.58/94.42	84.84/95.18	85.75/94.21
模型2	83.82/96.20	84.63/96.37	85.09/95.89	85.40/96.42
模型3	65.08/114.70	69.00/110.82	65.74/114.31	70.11/109.54
模型4	-	79.78/100.53	78.86/101.54	75.13/105.40
模型5	82.94/97.10	83.17/96.91	81.79/98.27	83.32/96.77
模型6	84.14/95.86	86.75/93.25	85.31/94.66	87.91/92.09

Table 2 A comparison of mesh generation time for different models of structured meshes/s

模型	TFI	MGNet^[31]+ 泊松方程	MGNet^[31]+ 双曲线方程	Ours
模型1	0.011	0.004	0.005	0.001
模型2	0.082	0.005	0.005	0.001
模型3	0.015	0.003	0.003	0.003
模型4	-	0.003	0.004	0.003
模型5	0.082	0.005	0.004	0.001
模型6	0.017	0.003	0.005	0.001

Fig. 6 Results of different unstructured mesh generation methods on model 1 ((a) Delaunay; (b) UMGPINN)

Fig. 7 Results of different unstructured mesh generation methods on model2 ((a) Delaunay; (b) UMGPINN)

Fig. 8 Results of 3D unstructured mesh generation on different models ((a) Model 1; (b) Model 2; (c) Model 3)

Table 3 A comparison of average min/max included angle for different models of unstructured meshes/(°)

模型	Delaunay	Ours
模型1	46.26/77.72	36.22/86.63
模型2	46.13/77.78	42.19/79.94
模型3	46.36/77.53	52.23/68.84
模型4	46.7/77.16	52.98/67.78
模型5	46.50/77.44	52.54/68.62
模型6	46.70/77.18	48.02/74.34

Table 4 A comparison of average aspect ratio for different models of unstructured meshes

模型	Delaunay	Ours
模型1	1.359	1.722
模型2	1.362	1.482
模型3	1.356	1.185
模型4	1.346	1.164
模型5	1.352	1.176
模型6	1.346	1.321

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