Multi-Solution Inverse Design of Pixelated Patch Antennas Using an Autoregressive Transformer

Young-Mok Yun; Seung-Won Shin; Jaeyong Chung; Kyung-Sik Choi

cs.LGOct 29, 2026

Multi-Solution Inverse Design of Pixelated Patch Antennas Using an Autoregressive Transformer

Authors: Young-Mok Yun, Seung-Won Shin, Jaeyong Chung, Kyung-Sik Choi

Organizations: Department of System Semiconductor Engineering, Yonsei University, Seoul 03722, South Korea.

Abstract

Deep-learning-based inverse design has emerged as a promising framework for pixelated patch antenna synthesis by enabling broader exploration of discrete geometry spaces and reducing design time compared with conventional template-based methods. Existing methods, including surrogate-assisted metaheuristic optimization, tandem inverse networks, and diffusion models, have advanced the field but still face practical limitations. Metaheuristic methods such as binary particle swarm optimization (BPSO) are sensitive to initialization and search hyperparameters and are often time-consuming, tandem networks have difficulty capturing the one-to-many nature of inverse antenna design, and diffusion models may require excessive complexity and data for moderate-scale binary layout synthesis. In this paper, an autoregressive (AR) transformer is presented for the inverse design of 10 x 10 pixelated patch antennas. Its sequential discrete generation process enables the synthesis of multiple feasible structures for a given target response. The pretrained model is further fine-tuned for dual-band design using step-shaped target responses with sharp spectral transitions, allowing intuitive band specification without manually constructing detailed S11 curves. Compared with BPSO, our proposed method generates valid and diverse antenna candidates more efficiently. Fabricated and measured examples confirm that distinct pixelated layouts can realize the desired antenna responses, thereby demonstrating the multi-solution capability of the proposed framework.

Figures & tables

Fig. 1: LLM-inspired autoregressive framework for antenna inverse design.

Fig. 2: Overview of the proposed framework.

Fig. 3: Pixel-spectrum paired dataset for training.

Fig. 4: Illustration of the autoregressive pixel generation process.

Fig. 5: Detailed architecture of the AR inverse model.

Fig. 6: Bit-level accuracy of the AR inverse model during training.

Fig. 7: BCE losses of the AR inverse model.

Fig. 8: Fine-tuning process of the AR inverse model.

Fig. 9: Forward surrogate model architecture.

Panel of Figure 10 — Fig. 10: Forward surrogate model training: (a) Loss curves (b) $S_{11}$ heatmap.

Fig. 11: Pixelated patch antenna geometry.

Fig. 12: Resonance ratio by density and spectrum distribution at 60% density.

Fig. 13: Conceptual illustration of the multi-armed bandit (MAB) problem.

Panel of Figure 14 — Fig. 14: Heatmaps of unique valid-candidate counts for searching algorithms: (a) multi-armed bandit, (b) random sampling, and (c) beam search.

Algorithm	Number of
top-ranked cases	Average full-band MSE
of best valid candidate
Multi-Armed Bandit	234 / 334	0.92
Random Sampling	78 / 334	1.19
Beam Search	22 / 334	1.67

TABLE I: Performance comparison of searching algorithms

Panel of Figure 16 — Fig. 15: Inverse design workflows of (a) BPSO-based iterative optimization and (b) AR transformer-based direct generation.

Panel of Figure 17 — Fig. 16: Heatmaps of unique valid-candidate counts over 334 dual-band test cases: (a) pretrained AR model, (b) BPSO best, and (c) BPSO worst.

Method	Successful
cases	Coverage
(%)	Redundant valid
candidates (%)	Average best
full-band MSE
Pretrained AR	322/334	96.4	0.0	0.89
BPSO (best)	202/334	60.5	20.4	7.67

TABLE II: Comparison of the pretrained AR model and BPSO variants

Panel of Figure 19 — Fig. 17: Heatmaps of unique valid-candidate counts for step-function targets: (a) fine-tuned AR model, (b) BPSO best, and (c) BPSO worst.

Method	Successful
cases	Coverage
(%)	Redundant valid
candidates (%)	Average best
notch MSE
Fine-tuned AR	111/153	72.5	0.0	40.15
BPSO (best)	59/153	38.6	3.5	55.66

TABLE III: Comparison of the fine-tuned AR model and BPSO variants

Fig. 18: Single-band antenna responses generated by the pretrained AR model.

Fig. 19: Dual-band antenna responses generated by the pretrained AR model.

Fig. 20: Multiple solutions for a single-band step-function target.

Fig. 21: Multiple solutions for a dual-band step-function target.

Fig. 22: Anechoic chamber setup for radiation pattern measurement.

Fig. 23: Measured results of the first 6-GHz single-band antenna: (a) fabricated antenna, (b) $S_{11}$ response, (c) Elevation radiation pattern ( $\phi=0^{\circ}$ ) at 6.01 GHz, (d) Elevation radiation pattern ( $\phi=90^{\circ}$ ) at 6.01 GHz.

Fig. 24: Measured results of the second 6-GHz single-band antenna: (a) fabricated antenna, (b) $S_{11}$ response, (c) Elevation radiation pattern ( $\phi=0^{\circ}$ ) at 5.99 GHz, (d) Elevation radiation pattern ( $\phi=90^{\circ}$ ) at 5.99 GHz.

Fig. 25: Measured results of the third 6-GHz single-band antenna: (a) fabricated antenna, (b) $S_{11}$ response, (c) Elevation radiation pattern ( $\phi=0^{\circ}$ ) at 6.02 GHz, (d) Elevation radiation pattern ( $\phi=90^{\circ}$ ) at 6.02 GHz.

Design	$f_{r}$ (GHz)	BW (MHz)	Realized Gain (dBi)
Design	$f_{r}$ (GHz)	BW (MHz)	$\phi=0^{\circ}$	$\phi=90^{\circ}$
First	6.01	170.20	5.38	5.67
Second	5.99	192.13	5.52	5.74
Third	6.02	139.36	5.32	5.98

TABLE IV: Measured performance of 6-GHz single-band antennas

Fig. 26: Measured results of the first dual-band antenna: (a) fabricated antenna, (b) $S_{11}$ response, Elevation radiation patterns at $f_{1}=5.91$ GHz (c) $\phi=0^{\circ}$ , (d) $\phi=90^{\circ}$ , and at $f_{2}=6.85$ GHz (e) $\phi=0^{\circ}$ , (f) $\phi=90^{\circ}$ .

Fig. 27: Measured results of the second dual-band antenna: (a) fabricated antenna, (b) $S_{11}$ response, Elevation radiation patterns at $f_{1}=5.94$ GHz (c) $\phi=0^{\circ}$ , (d) $\phi=90^{\circ}$ , and at $f_{2}=6.88$ GHz (e) $\phi=0^{\circ}$ , (f) $\phi=90^{\circ}$ .

Fig. 28: Measured results of the third dual-band antenna: (a) fabricated antenna, (b) $S_{11}$ response, Elevation radiation patterns at $f_{1}=5.87$ GHz (c) $\phi=0^{\circ}$ , (d) $\phi=90^{\circ}$ , and at $f_{2}=6.86$ GHz (e) $\phi=0^{\circ}$ , (f) $\phi=90^{\circ}$ .

Design	Band	$f_{r}$ (GHz)	BW (MHz)	Realized Gain (dBi)
Design	Band	$f_{r}$ (GHz)	BW (MHz)	$\phi=0^{\circ}$	$\phi=90^{\circ}$
First	Lower	5.91	106.85	5.81	5.91
First	Upper	6.85	152.08	4.46	4.35
Second	Lower	5.94	89.53	5.26	5.33
Second	Upper	6.88	169.03	4.54	4.36
Third	Lower	5.87	173.76	5.43	5.50

TABLE V: Measured performance of dual-band antennas

Target set	Method	Mean normalized Hamming distance
Original targets	Pretrained AR	0.4540
	BPSO (best)	0.1351
	BPSO (worst)	0.1174
	VBPSO	0.2680
	MVBPSO	0.1678
Step-shaped targets	Fine-tuned AR	0.4605

TABLE VI: Structural diversity based on normalized Hamming distance

Ref.	Design
Method	Multiple
solutions	Step-function
target	Average
synthesis time	Antenna
type	Substrate /
height	$f_{1}/f_{2}$

TABLE VII: Comparison with state-of-the-art dual-band antenna works in terms of design methodology and antenna performance

Young-Mok Yun received the B.S. degree in electrical and electronic engineering from Hongik University, Seoul, South Korea, in 2025. He is currently working toward the M.S. degree in system semiconductor engineering at Yonsei University. His current research interests include AI-assisted inverse design and optimization of RF/millimeter-wave components and high-speed interface systems.

Table 36

Seung-Won Shin received the B.S. degree in electrical and electronic engineering from Yonsei University, Seoul, South Korea, in 2026. He is currently working toward the M.S. degree in system semiconductor engineering at Yonsei University. His current research interests include AI-assisted integrated circuit design and machine-learning-based electronic design automation.

Table 37

Jaeyong Chung (Member, IEEE) received the B.S. degree in electrical engineering from Yonsei University, Seoul, South Korea, in 2006, and the M.S. and Ph.D. degrees in electrical and computer engineering from the Department of Electrical and Computer Engineering, University of Texas at Austin, Austin, TX, USA, in 2008 and 2011, respectively. He worked with the Strategic CAD Lab (SCL), Intel, and the IBM Thomas J. Watson Research Center in Summer 2008 and Summer 2010, respectively. From 2011 to 2013, he was with the Design Compiler Team, Synopsys, Inc., Mountain View, CA, USA. He is currently an Associate Professor with Yonsei University, Seoul, South Korea. His current research interests include efficient deep learning and AI-based hardware design.

Table 38

Kyung-Sik Choi (Member, IEEE) received the B.S., M.S., and Ph.D. degrees in electrical engineering from Korea Advanced Institute of Science and Technology (KAIST), Daejeon, South Korea, in 2016, 2018, and 2022, respectively. From 2022 to 2024, he was a Post-Doctoral Researcher with ETH Zurich, Zürich, Switzerland. From 2024 to 2025, he was a tenure-track Assistant Professor with the Department of Electronic Engineering, Seoul National University of Science and Technology (SeoulTech), Seoul, South Korea. Since 2025, he has been a tenure-track Assistant Professor with the Department of System Semiconductor Engineering, Yonsei University, Seoul, South Korea. His research interests include radio frequency (RF) integrated circuits and systems, as well as high-frequency terahertz integrated circuits and systems based on complementary metal–oxide–semiconductor (CMOS) technology.

Table 39

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Machine Learning Assisted Inverse Design of Pixelated mmWave Patch Antennas

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A machine learning-assisted framework for the inverse design of pixelated millimetre-wave patch antennas targeting the 22--30 GHz band is presented. The antenna surface is represented as a 19x23 binary pixel grid on a Rogers RT/duroid 5880 substrate, where each pixel is either metal or empty, with a continuous electrical path from the feed enforced by design. An initial dataset of approximately 6,000 full-wave CST simulations was collected from structured random pixel patterns, of which only around 40% achieved a resonance with |S11| <= -10 dB anywhere in the band, resulting in an imbalanced dataset. To improve simulation efficiency, an XGBoost binary classifier was trained on this data to distinguish resonant from non-resonant patterns before simulation. Using the classifier as a pre-simulation filter, an additional 4,000 patterns were selected and simulated, raising the overall proportion of resonant designs in the combined 10,000-sample dataset from approximately 40% to 52%. A hybrid CNN-BiLSTM forward surrogate was then trained on this augmented dataset to predict the full complex S11 response across 801 frequency points, using a physics-guided composite loss that explicitly emphasises resonance dip accuracy. Finally, an inverse design model was developed that optimises in a compact 64-dimensional latent space using gradient descent to generate pixel patterns matching a desired S11 specification. The results show good agreement between the surrogate-predicted and CST-simulated |S11| responses for the generated designs and demonstrate the feasibility of automatically designing and reconfiguring antenna structures.

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