AI Pixel Antennas

Deep learning-enabled inverse design of compact pixelated antennas using tandem neural networks, transfer learning, and or evolutionary algorithms.

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Authors

Aggraj Gupta and Uday Khankhoje Department of Electrical Engineering Indian Institute of Technology Madras

Contact:

• Aggraj Gupta: gupta.aggraj@gmail.com
• Uday Khankhoje: uday@ee.iitm.ac.in

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Overview

This repository provides complete workflows for neural network-based inverse design of pixelated microstrip antennas. The methods enable rapid synthesis of compact single-band and multi-band antennas from desired electromagnetic specifications through either a tandem neural network architecture or a neural-network backed evolutionary optimization approach. The key work has ben published in the IEEE Transactions on Antennas & Propagation and the IEEE Journal on Multiscale and Multiphysics Computational Techniques (see detailed information below).

Key Features

• Tandem Neural Network Architecture: Combines inverse and forward surrogate models to resolve non-uniqueness in inverse design
• Binary Pixelated Parameterization: 12×12 pixel grid representation enabling exploration of 2^142 possible designs
• Transfer Learning Framework: Reduces required simulations by 88% when adapting from air to dielectric substrates
• Multiple Design Methods: Supports both neural network-based and evolutionary (BPSO) optimization approaches
• Rapid Design Generation: Sub-second antenna synthesis compared to hours of traditional optimization

Traditional trial-and-error vs. tandem neural network-based inverse synthesis

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Publications

This code implements methods described in the following peer-reviewed publications:

1. Base Paper: Tandem Neural Network Design

"Tandem Neural Network based Design of Multi-band Antennas" Aggraj Gupta, Chandan Bhat, Emir Karahan, Kaushik Sengupta, Uday Khankhoje IEEE Transactions on Antennas and Propagation, vol. 71, no. 8, pp. 6308-6317, 2023 DOI: 10.1109/TAP.2023.3276524

Key Contributions:

• Tandem architecture combining inverse network with frozen forward surrogate
• Smooth thresholding activation for binary design enforcement
• Joint loss function balancing spectrum fidelity, design consistency, and binary regularization

2. Transfer Learning Extension

"Transfer Learning Based Rapid Design of Frequency and Dielectric Agile Antennas" Aggraj Gupta, Uday Khankhoje IEEE Journal on Multiscale and Multiphysics Computational Techniques, vol. 10, pp. 47-57, 2024 DOI: 10.1109/JMMCT.2024.3509773

Key Contributions:

• Transfer learning strategy leveraging fast air-substrate simulations
• Scaling laws for frequency and dielectric migration
• 88% reduction in required dielectric simulations (from 500k to 60k samples)

Related Work: Multi-Port RF Systems

"Deep-learning Enabled Generalized Inverse Design of Multi-Port Radio-frequency and Sub-Terahertz Passives and Integrated Circuits" Emir Karahan, Zheng Liu, Aggraj Gupta, Zijian Shao, Jonathan Zhou, Uday Khankhoje, Kaushik Sengupta Nature Communications, vol. 15, article 10734, 2024 DOI: 10.1038/s41467-024-54178-1

This publication demonstrates the broader applicability of the surrogate-based inverse design paradigm to filters, couplers, and impedance matching networks.

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Patent Information

IMPORTANT: The algorithms implemented in this code are protected by patent. See PATENT_NOTICE for complete details.

Patent: Method Of Designing Ultra Compact Single Band Antennas Inventors: Uday Khankhoje and Aggraj Gupta Indian Patent No. 572928 (Filed: 22 Jan 2024, Granted: 30 Oct 2025)

• Academic/Research Use: Free with proper attribution (cite papers above)
• Commercial Use: Requires separate patent license (contact authors)

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Technical Overview

Pixelated Antenna Model

• Base patch tessellated into 12×12 binary pixels
• Each pixel represents metal (1) or no-metal (0)
• Feed-adjacent pixels fixed to ensure connectivity
• Avoids template bias, enables non-intuitive geometries

Tandem Neural Network Architecture

The tandem architecture consists of:

1. Inverse Network: Maps desired S₁₁(f) spectrum → pixelated geometry
2. Forward CNN Surrogate: Maps geometry → S₁₁(f) (frozen weights)
3. Joint Training: Ensures data consistency despite non-unique inverse mapping

Loss Function:

L = L_S + α·L_D + β·L_B

• L_S: Spectrum prediction error
• L_D: Design consistency error
• L_B: Binary regularization term

Smooth Thresholding Activation:

f(x) = 0.5 + 0.5·tanh(m(x - 0.5))

Enforces binary outputs during training, not as post-processing.

Transfer Learning Strategy

Motivation: Air-filled simulations are 50-60× faster than dielectric simulations.

Workflow:

1. Train forward CNN on 500k air-filled antennas (10-20 GHz)
2. Apply scaling laws to map air designs to dielectric domain
3. Fine-tune with 60k dielectric antennas (FR-4, 1-5 GHz)
4. Achieve 88% reduction in simulation cost

Scaling Law:

w_d = a·w_a,  where  a = f_a / (f_d·√ε_eff)

Typical scale factors: 2-5 for migration from 10-20 GHz (air) to 1-5 GHz (FR-4).

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Repository Contents

MATLAB Code Files

File	Function Signature	Description
generateantenna_air.m	p = generateantenna_air(x_dis, y_dis, ant_des)	Generate single air-substrate antenna structure
generateantenna_for_tandem_air.m	generateantenna_for_tandem_air(x_dis, y_dis, samples_to_generate)	Generate dataset of air-substrate antennas in parallel
generateantenna_scaled.m	p = generateantenna_scaled(x_dis, y_dis, ant_des)	Generate single dielectric-substrate antenna with scaling
generateantenna_transferlearning.m	generateantenna_transferlearning(x_dis, y_dis, samples_to_generate)	Generate dielectric antenna dataset for transfer learning
inverse_design_using_bpso_with_TLfwdmodel.m	Script (no function)	Evolutionary inverse design using Binary PSO with neural surrogate
parsave.m	parsave(fname, Test_patches, spec)	Helper function for parallel dataset saving

Function Parameters:

• x_dis, y_dis: Grid discretization (number of pixels + 1, typically 13)
• ant_des: 12×12 binary matrix specifying antenna geometry
• samples_to_generate: Number of antenna samples to simulate
• fname: Output filename for saved data
• Test_patches: Flattened antenna design vector (144 elements)
• spec: S₁₁ spectrum (81 frequency points)

Returns:

• p: MATLAB pcbStack object representing complete antenna structure

Python/Jupyter Notebooks

File	Description
Inverse_design_tandem.ipynb	Training code for tandem neural network (forward + inverse)
Test_Inverse_design_tandem.ipynb	Inference code to generate antenna designs from target spectra
Forward_model_Transfer_learning.ipynb	Transfer learning implementation for dielectric substrates

Pre-trained Models

Note: Due to file size limitations, pre-trained models are hosted externally. Download links:

File	Description	Size	Download Link
Forward_model_for_tandem.pth	Forward surrogate CNN for tandem network (air, 10-20 GHz)	512 MB	Download
inverse_tandem_model.pth	Inverse network for tandem architecture	63 MB	Download
TLfwdmodel	Transfer learning forward surrogate (FR-4, 1-5 GHz)	171 MB	Download

After downloading, place these files in the root directory of the repository.

Datasets

Note: Due to file size limitations, datasets are hosted externally. Download links:

File	Description	Size	Download Link
antenna_dataset.mat	Air-substrate antenna database (500k samples)	436 MB	Download

After downloading, place this file in the root directory of the repository.

Figures

High-resolution images illustrating the methodology:

• tandem_overview.png - Conceptual comparison: traditional vs. AI-based design
• tandem_architecture.png - Detailed tandem network architecture diagram
• forward_cnn.png - Forward surrogate CNN structure
• transfer_learning_flow.png - Transfer learning workflow
• pixelated_patch.png - Pixelated antenna representation
• single_band_result.png - Example single-band antenna design result

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Usage Guide

Prerequisites

MATLAB Requirements:

• MATLAB R2020b or later
• Antenna Toolbox
• Parallel Computing Toolbox (for dataset generation)

Python Requirements:

• Python 3.8+
• PyTorch 1.10+
• NumPy, Matplotlib
• Jupyter Notebook

Use Case 1: Generate Single Air-Substrate Antenna

Create and visualize a single antenna structure on air substrate:

% Define a 12×12 binary antenna design
ant_design = randi([0,1], 12, 12);
ant_design(6:7, 1) = 1;  % Ensure feed connectivity

% Generate antenna structure (13 = 12 pixels + 1)
antenna = generateantenna_air(13, 13, ant_design);

% Simulate S-parameters
freq = linspace(10e9, 20e9, 81);
s = sparameters(antenna, freq, 50);
rfplot(s, 1, 1);

Inputs:

• 13, 13: Grid dimensions (12×12 pixels requires 13 grid points)
• ant_design: 12×12 binary matrix (1=metal, 0=no metal)

Outputs:

• antenna: pcbStack object with air substrate, ready for EM simulation

Use Case 2: Generate Air-Substrate Dataset

Create a large dataset for neural network training:

% Generate 1000 random air-substrate antennas
generateantenna_for_tandem_air(13, 13, 1000);

% Output: Individual .mat files (output1.mat, output2.mat, ...)
% Each contains: Test_patches (144×1 design vector), spec (81×1 S11 spectrum)

Note: Uses 8 parallel workers. Adjust parpool('local', 8) based on available cores.

Use Case 3: Transfer Learning for Dielectric Substrates

Scale air-substrate designs to FR-4 and generate dielectric dataset:

% First, create scaled dielectric design
ant_design = randi([0,1], 12, 12);
ant_design(6:7, 1) = 1;

% Generate FR-4 antenna (scaling factor a=4 built-in)
antenna_fr4 = generateantenna_scaled(13, 13, ant_design);

% Generate full dataset for transfer learning
generateantenna_transferlearning(13, 13, 5000);

Substrate Parameters (built-in):

• Material: FR-4
• ε_r = 4.8, tan δ = 0.026
• Thickness: 3.2 mm
• Frequency range: 1-5 GHz

Use Case 4: Inverse Design Using Tandem Neural Network

Generate antenna from desired spectrum using pre-trained model:

% See Test_Inverse_design_tandem.ipynb for complete workflow

Python workflow:

1. Load pre-trained models (Forward_model_for_tandem.pth, inverse_tandem_model.pth)
2. Define target S₁₁(f) spectrum (81 frequency points)
3. Run inverse network to generate 12×12 design
4. Validate using forward surrogate
5. Export to MATLAB for final EM verification

Use Case 5: Evolutionary Inverse Design (BPSO)

Use Binary Particle Swarm Optimization with neural surrogate:

% Open and configure inverse_design_using_bpso_with_TLfwdmodel.m
% Set target frequency (line 11):
center_fiu = find(freq == 3.6e9);  % Target: 3.6 GHz

% Set band type (lines 20-26):
% - Single band: pass_band = [center_fiu-4:center_fiu+4]
% - Dual band: uncomment dual band section

% Run script (outputs best design and convergence plot)
run('inverse_design_using_bpso_with_TLfwdmodel.m')

Algorithm Parameters:

• Population size: 1000
• Max iterations: 50
• Inertia weight: 0.9 → 0.4 (linearly decreasing)
• Acceleration factors: c1=c2=2

Output:

• antenna_des: Optimized 12×12 binary design
• output_new: Predicted S₁₁ spectrum
• Convergence plot and S₁₁ response plot

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Example Results

Single-Band Antenna (3.6 GHz, FR-4)

Performance Metrics:

• Resonant frequency: 3.6 GHz
• Return loss: < -20 dB
• Fractional bandwidth: ~5%
• Gain: ~3.5 dBi
• Radiation efficiency: > 70%

Multi-Band Capabilities

The tandem network can synthesize dual-band and triple-band antennas with:

• Independent control of resonant frequencies
• Up to 50% area reduction vs. conventional patches
• Compact, non-intuitive geometries

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Important Notes and Limitations

Scope of Implementation

The code provided in this repository covers specific use cases:

• 12×12 pixelated microstrip antennas
• Air and FR-4 substrates
• Frequency ranges: 10-20 GHz (air), 1-5 GHz (FR-4)
• Single-band and limited multi-band designs

The algorithms in the published papers can be instantiated in many other settings NOT covered in this repository, including:

• Different pixel grid resolutions (e.g., 16×16, 24×24)
• Alternative substrate materials (Rogers, alumina, etc.)
• Different frequency bands (sub-GHz, mmWave, sub-THz)
• Other antenna types (slots, monopoles, arrays)
• Different EM objectives (gain, efficiency, radiation patterns)
• Multi-port networks and RF passives (see Nature Comm. paper)

Computational Requirements

• Dataset generation: Computationally intensive; 500k air antennas ≈ weeks on 8-core workstation
• Pre-trained models provided: Use these to avoid re-training
• Neural network training: Requires GPU (8+ GB VRAM recommended)
• Inference: Fast on CPU (< 1 second per design)

Validation

All neural network predictions should be validated with full-wave EM simulation before fabrication. The surrogate models provide excellent approximations but may have errors for edge cases or out-of-distribution designs.

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How to Cite

If you use this code or methodology in your research, please cite the relevant publications:

For Tandem Neural Network Method:

@article{gupta2023tandem,
  title={Tandem Neural Network Based Design of Multi-band Antennas},
  author={Gupta, Aggraj and Bhat, Chandan and Karahan, Emir and Sengupta, Kaushik and Khankhoje, Uday},
  journal={IEEE Transactions on Antennas and Propagation},
  volume={71},
  number={8},
  pages={6308--6317},
  year={2023},
  doi={10.1109/TAP.2023.3276524}
}

For Transfer Learning Method:

@article{gupta2024transfer,
  title={Transfer Learning Based Rapid Design of Frequency and Dielectric Agile Antennas},
  author={Gupta, Aggraj and Khankhoje, Uday},
  journal={IEEE Journal on Multiscale and Multiphysics Computational Techniques},
  volume={10},
  pages={47--57},
  year={2024},
  doi={10.1109/JMMCT.2024.3509773}
}

For Related Multi-Port RF Systems:

@article{karahan2024deep,
  title={Deep-learning Enabled Generalized Inverse Design of Multi-Port Radio-frequency and Sub-Terahertz Passives and Integrated Circuits},
  author={Karahan, Emir Ali and Liu, Zheng and Gupta, Aggraj and Shao, Zijian and Zhou, Jonathan and Khankhoje, Uday and Sengupta, Kaushik},
  journal={Nature Communications},
  volume={15},
  number={1},
  pages={10734},
  year={2024},
  doi={10.1038/s41467-024-54178-1}
}

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License and Patent Information

Copyright License

This software is licensed under the MIT License (No Patent Grant). See LICENSE file for complete terms.

In brief: You may freely use, modify, and distribute the source code, but WITHOUT any patent rights.

Patent Notice

The copyright license does NOT include any patent license. The algorithms implemented in this code are protected by Indian Patent No. 572928.

• Academic/Non-Commercial Use: Encouraged with proper citation
• Commercial/Industrial Use: Requires separate patent license

See PATENT_NOTICE for complete details and contact information for commercial licensing.

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Acknowledgments

This work was supported by research funding at IIT Madras and a research grant “6G: Sub-THz Wireless Communication with Intelligent Reflecting Surfaces (IRS)” numbered R‐23011/3/2022‐CC&BT‐MeitY by the Ministry of Electronics and Information Technology (MeitY), Government of India. We thank our collaborators at Princeton University (Prof. Kaushik Sengupta's group) for contributions to the foundational research.

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Questions and Support

For technical questions about the code:

• Open an issue in this repository (when public)
• Contact: gupta.aggraj@gmail.com

For patent licensing inquiries:

• Contact: uday@ee.iitm.ac.in

For academic collaborations:

• Contact either author via emails above

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Last Updated: February 2026