Opto-Electronic Engineering, Volume. 52, Issue 4, 250058(2025)
Adaptive mesh partitioning for graph attention Transformer networks
Figures & Tables(11)
Fig. 1. Process of adaptive mesh refinement under node classification problem
Fig. 4. Bessel's equations. (a) Original mesh; (b) Solution field (original mesh); (c) Gradient error distribution (original mesh); (d) GTF-Net mesh; (e) Solution field (GTF-Net mesh); (f) Error gradient distribution (GTF-Net mesh); (g) skFem mesh; (h) Solution field (skFem mesh); (i) Gradient error distribution (skFem mesh)
Fig. 5. Solving optical waveguide. (a) Original mesh; (b) Solution field (original mesh); (c) Gradient error distribution (original mesh); (d) GTF-Net mesh; (e) Solution field (GTF-Net mesh); (f) Error gradient distribution (GTF-Net mesh); (g) skFem mesh; (h) Solution field (skFem mesh); (i) Gradient error distribution (skFem mesh)
Fig. 6. Quality distribution of different mesh cells. (a) SICN value distribution of original mesh cells; (b) SICN value distribution of GTF-Net mesh cells; (c) SICN value distribution of skFem mesh cells; (d) Gamma value distribution of original mesh cells; (e) Gamma value distribution of GTF-Net mesh cells; (f) Gamma value distribution of skFem mesh cells; (g) SIGE value distribution of original mesh cells; (h) SIGE value distribution of GTF-Net mesh cells; (i) SIGE value distribution of skFem mesh cells
Table 1. Part of random function in training data generation method
View tableView in ArticleTable 1. Part of random function in training data generation method
Function name Description plane_wave( ) Generate two-dimensional plane wave, using cosine function to represent the propagation of electromagnetic waves. cylindrical_wave( ) Generate cylindrical wave, where the wave intensity is related to the radial distance from the source point, described using Bessel function. random_waveguide_field() Generate random waveguide field, providing random refractive index and waveguide parameter. gaussian_beam( ) Generate Gaussian beam, calculate the radial distance, and adjust the beam width based on propagation distance. random_interface_field( ) Generate random interface field, selecting random interface types and Gaussian beams as base field. step_interface( ) Define step interface, determining the change in dielectric constant of material at boundary position. periodic_interface( ) Define periodic interface, producing periodic material structure. multipole_field( ) Define multipole field, using Bessel function and angle to describe multipoles of different orders. evanescent_wave( ) Define evanescent wave, primarily decaying in the y-direction.
Table 2. Parameter setting for different neural network frameworks
View tableView in ArticleTable 2. Parameter setting for different neural network frameworks
Parameter GTF-Net TF-Net GATv2-Net Feature encoder Dense Dense Dense Transformer layer 4-layer TransformerConv 8-layer TransformerConv None GATv2 layer 4-layer GATv2Conv None 8-layer GATv2Conv Skip connections 4 dense skip connections 4 dense skip connections 4 dense skip connections Layer normalization 8-layer LayerNorm 8-layer LayerNorm 8-layer LayerNorm Feature aggregation Dense -> ReLU -> Dropout Dense -> ReLU -> Dropout Dense -> ReLU -> Dropout Classifier Dense Dense Dense Activation function ReLU, Sigmoid ReLU, Sigmoid ReLU, Sigmoid Dropout 0.1 0.1 0.1
Table 3. Performance comparison of GTF-Net with other methods
View tableView in ArticleTable 3. Performance comparison of GTF-Net with other methods
Network MSE/% Accuracy/% F1-Score/% GTF-Net 1.52 97.9 96.4 TF-Net 1.86 97.5 95.7 GATv2-Net 3.12 95.9 94.2
Table 4. Error comparison between GTF-Net Grid and other methods
View tableView in ArticleTable 4. Error comparison between GTF-Net Grid and other methods
Mesh Bessel equations Original mesh Number of nodes Number of elements Standard deviation Time/s Ratio/% Number of nodes Number of elements Standard deviation Time/s Ratio/% Original mesh 98 162 0.016 — — 98 162 0.031 — — skFem 3474 6842 2.384×10−4 5.46 — 873 1728 3.379×10−5 6.43 — GTF-Net 3489 6825 3.353×10−5 3.51 35.74 874 1714 2.573×10−5 2.58 59.91
Table 5. Element quality analysis of different meshes
View tableView in ArticleTable 5. Element quality analysis of different meshes
Quality parameter Original mesh GTF-Net mesh skFem mesh SICN 0.9736 (0.8311->1) 0.9644 (0.362->1) 0.866 (0.866->0.866) Gamma 0.9685 (0.7812->1) 0.9622 (0.3179->1) 0.8284 (0.8284->0.8284) SIGE 0.9884 (0.9068->1) 0.9874 (0.6281->1) 0.9292 (0.9292->0.9292)
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Ting Han, Jia Ye, Lianshan Yan, Zongxin Gan. Adaptive mesh partitioning for graph attention Transformer networks[J]. Opto-Electronic Engineering, 2025, 52(4): 250058
Paper Information
Category: Article
Received: Feb. 27, 2025
Accepted: Apr. 10, 2025
Published Online: Jun. 11, 2025
The Author Email: Jia Ye (叶佳)
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