Physics-Augmented Graph Transformers for Patch-Antenna Forward and Inverse Design

Avi Epstein; Snir Nehemia; Haim Suchowski; Lior Wolf

cs.LGOct 4, 2026

Physics-Augmented Graph Transformers for Patch-Antenna Forward and Inverse Design

Authors: Avi Epstein, Snir Nehemia, Haim Suchowski, Lior Wolf

Organizations: Tel Aviv University

Abstract

Full-wave electromagnetic (EM) simulation enables accurate patch-antenna analysis but is computationally expensive for large-scale forward prediction and inverse design. We present a mesh-native, physics-augmented graph-learning framework that treats radiation-pattern prediction as signal reconstruction on an irregular surface mesh. For the forward problem, a GPS graph transformer is trained with Physics-Augmented Intermediate Supervision (PAIS), an auxiliary node-level objective that predicts complex surface currents, the physical intermediate linking geometry to radiation. PAIS improves multiple GNN backbones at no inference-time cost, while shuffled-current and non-physical controls show the gain comes from physical correspondence. Direction-conditioned decoding and a differentiable radiation-integral consistency loss further exploit this structure. On an 80,000-sample CST benchmark, GPS+PAIS reaches MSE 0.17 / PSNR 19.67, generalizes to a PCA split, and transfers zero-shot to canonical patches. For inverse design, surrogate-filtered diffusion beats nearest-neighbor retrieval by 32% relative MSE.

Figures & tables

Fig. 1 : Antenna learning and inverse-design pipeline. (a) Example geometry; (b) component-wise surface currents. (c) Forward: mesh graph $G$ $\to$ GPS with surface-current supervision $\vec{J}$ $\to$ pattern $F$ . (d) Inverse: target $F$ conditions a diffusion U-Net; candidates are ranked by the surrogate and validated in CST to select $G$ .

Model	MAE $\downarrow$	MSE $\downarrow$	MS-SSIM $\uparrow$	PSNR $\uparrow$
Nearest neighbor	0.60	1.00	0.70	9.54
MLP	0.45	0.55	0.81	14.11
U-Net	0.45	0.53	0.81	14.23
ResNet-50	0.46	0.56	0.80	14.00
GCN	0.44	0.53	0.81	14.46
GCN + PAIS	0.43	0.50	0.82	14.63

Table 1 : Forward radiation-pattern prediction on FMNIST+CIFAR (random split, 5.6 GHz). Lower is better for MAE/MSE; higher for MS-SSIM/PSNR. “+PAIS”: Physics-Augmented Intermediate Supervision; “pos. aux”/“shuffled SC” are controls (node coordinates / permuted currents); “+Directional” and “+Phys” add the direction-conditioned decoder and physics-consistency loss (Sec. 4.1 ). Best in bold; DGCNN, MGN and GPS rows are means over 3 seeds (std

\leq 0.01

for MAE/MSE/MS-SSIM and

\leq 0.18

dB for PSNR); the matched-size mixture row uses one seed.

Fig. 2 : Zero-shot predictions on square patch antennas with a parasitic element. Each row: ground-truth pattern (left), prediction with surface-current information (center), and without it (right); MSE is shown lower-left of each prediction.

Method	MAE $\downarrow$	MSE $\downarrow$	MS-SSIM $\uparrow$	PSNR $\uparrow$	HPBW-IoU $\uparrow$
NN	0.61	1.13	0.85	9.02	0.53
NN-seeded SA + surr.	0.59	1.49	0.83	9.13	0.52
CMA	0.85	2.76	0.70	6.00	0.23
GA + surr.	0.94	3.30	0.65	4.99	0.16
SA + surr.	0.95	3.09	0.65	5.08	0.18
Diff. – 5 rand.	0.70	1.95	0.79	7.45	0.36

Table 2 : Inverse design on the 100 hardest PCA-split targets. All rows except “GNN eval.” are CST-validated against ground truth. GA/SA: genetic algorithm / simulated annealing over the two

16{\times}16

matrices under the same 500-evaluation budget; NN-seeded SA starts from the nearest training antenna. “Diff. – 5 rand.”: 5 unfiltered diffusion samples. “GNN eval.”: the surrogate’s own score of the selected candidate.

Method	MSE $\downarrow$	MAE $\downarrow$	PSNR $\uparrow$	MS-SSIM $\uparrow$	HPBW-IoU $\uparrow$
NN (simulated)	0.65	0.48	11.33	0.88	0.68
Optimized (simulated)	0.56	0.41	12.74	0.87	0.79

Table 3 : Inverse design on the 500 hardest PCA split targets. “Optimized (simulated)” is the best of the top-5 surrogate selected candidates, validated in EM simulation.

Fig. 3 : Hand-designed targets ( $w{=}2$ ). Columns: surrogate-filtered diffusion output (CST-simulated), target, and nearest-neighbor retrieval. Top: multi-lobe target; bottom: broad-lobe target.

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Abstract

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