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Machine Learning Assisted Inverse Design of Pixelated mmWave Patch Antennas

Nadeem Rather, Holger Claussen, Lester Ho

arXiv:2608.23469v1eess.SPcs.AI

TL;DR

Pixelated mmWave antenna design faces an exponentially large layout space, costly full-wave simulation, and imbalanced resonance data. The paper combines classifier-guided augmentation, a CNN-BiLSTM surrogate, and 64-dimensional latent-space optimisation. All four CST-validated designs met the target-band |S11| objective, with three showing small frequency and depth errors.

  • Problem

    Pixelated antenna design requires searching exponentially many layouts while full-wave electromagnetic simulations are expensive and random layouts often yield imbalanced resonance data.

  • Method

    The framework uses XGBoost pre-simulation filtering, a physics-guided CNN-BiLSTM surrogate, and gradient descent through a frozen surrogate in a 64-dimensional autoencoder latent space.

  • Results

    All four CST-simulated patterns achieved |S11| ≤−10 dB within their specified target bands; three had frequency errors below 0.2 GHz and depth errors below 1.5 dB.

  • Takeaways & Limitations

    The pipeline demonstrates feasible automatic generation of connected, feed-attached pixel patterns resonating within specified target bands across 22–30 GHz.

Abstract

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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.

I. INTRODUCTION

Pixelated antennas expand the design space beyond conventional patch geometries but make exhaustive electromagnetic evaluation impractical. The paper presents an integrated machine-learning pipeline to improve data generation, surrogate modelling, and inverse design for 22–30 GHz antennas.

  • Conventional patch geometries simplify fabrication but limit the range of radiating topologies once the substrate and feed are fixed.
  • Pixelated structures enable nonconventional geometries and potentially improved impedance matching, bandwidth, or radiation characteristics.
  • 300 pixels create a search space of 2^300 layouts, while each full-wave simulation may require several minutes.These costs make exhaustive evaluation impractical.
  • Random pixel layouts often produce non-useful resonances, causing highly imbalanced datasets and inefficient use of simulation resources.One cited study found usable resonance in only 12.6% of more than 150,000 random layouts.
  • The proposed end-to-end pipeline combines ML-assisted dataset augmentation, a CNN-BiLSTM complex-S11 surrogate, and latent-space inverse design for 22–30 GHz antennas.

II. ANTENNA STRUCTURE AND DATASET

The antenna uses a constrained pixelated copper surface on Rogers RT/duroid 5880, with structured-random generation used to provide connected and topologically diverse training patterns. CST simulations sample complex S11 over the 22–30 GHz band.

  • The antenna substrate is 16×12.5 mm2 Rogers RT/duroid 5880 with εr=2.2, loss tangent tan δ=0.0009, and thickness h=0.508 mm.The copper thickness is t=0.035 mm.
  • The active surface contains a 19×23 grid of 0.5×0.5 mm2 copper pixels, while a fixed feed line occupies columns 1–11 of the centre row.
  • Structured-random generation uses seven topology families to cover broad regions of the design space.The families include rect block, rect ring, split ring, symmetric mirror, stub patch, scatter connected, and inset patch.
  • Each generated pattern enforces at least 20 active pixels and constraints intended to preserve a connected metal path to the feed.
  • CST simulations use a time-domain solver over 22–30 GHz and export complex S11 at 801 uniformly spaced frequency points per design.

III. MACHINE LEARNING MODELLING

The modelling workflow has three sequential phases: classifier-guided dataset augmentation, forward surrogate training, and latent-space inverse optimisation.

  • The machine-learning workflow comprises classifier-guided dataset augmentation, forward surrogate training, and latent-space inverse optimisation.

A. Classifier-Guided Data Augmentation

Classifier-guided augmentation addresses the initial imbalance by identifying promising patterns before CST simulation. XGBoost was selected as the screening model, and the augmented dataset increased the resonant-design proportion.

  • Approximately 6,000 structured-random patterns were simulated and labelled resonant when their minimum |S11| fell below −10 dB anywhere in 22–30 GHz.
  • Approximately 40% of the initial patterns were resonant, leaving the dataset heavily skewed toward non-resonant designs.
  • XGBoost was selected from five evaluated binary classifiers for screening new patterns before CST simulation.The evaluation used accuracy, macro F1-score, ROC AUC, and the train-to-validation accuracy gap.
  • Random Forest achieved higher accuracy but had a 14.7% train-to-validation gap, suggesting overfitting and reduced reliability on unseen patterns.
  • An additional 4,000 classifier-selected patterns expanded the dataset to approximately 10,000 samples and increased the resonant proportion from approximately 40% to 52%.

B. Forward Surrogate Model (CNN-BiLSTM)

The forward surrogate maps each binary 19×23 antenna pattern to its full complex S11 spectrum over 801 frequency points. Its composite loss combines complex-response, magnitude, resonance, and smoothness terms, with explicit emphasis on resonance dip accuracy.

  • Architecture: The CNN-BiLSTM surrogate maps a binary 19×23 pixel pattern to an 801-point complex S11 spectrum over 22–30 GHz.A convolutional spatial encoder extracts geometric features, while the frequency projection head and bidirectional LSTM model frequency-dependent structure.
  • Architecture: The spatial encoder uses three Conv2D–BatchNorm–GELU blocks with residual blocks and channel depths progressing from 1 to 256.Global average pooling produces a 256-dimensional feature vector for the frequency projection head.
  • Loss function: The composite loss combines complex S11 MSE, dB-magnitude Huber loss, resonance-depth L1 loss, resonance-frequency L1 loss, and spectrum-slope MSE.Resonance depth and frequency terms are evaluated on samples with true |S11|dB < −10 dB.
  • Loss function: The resonance-frequency term uses a differentiable soft-argmin, while the slope term penalises non-smooth predictions inconsistent with real EM responses.The loss weights are (λ1, λ2, λ3, λ4, λ5)=(1.0, 2.0, 4.0, 15.0, 0.3).

3) Training:

The surrogate is trained on stratified data with early stopping, controlled optimisation, class-aware sampling, and geometric augmentation. These procedures address dataset imbalance while regularising training.

  • Training setup: The 10,000-sample dataset is split stratified 70/15/15 into approximately 7,000 training, 1,500 validation, and 1,500 test samples.Training uses seed 42 and early stopping after 30 epochs without improvement.
  • Training setup: AdamW training uses a peak learning rate of 5×10^-5 and weight decay of 10^-4, with linear warm-up followed by cosine decay.The learning rate is increased linearly during the first 3 epochs before cosine decay.
  • Model: The CNN-BiLSTM architecture combines spatial encoding, frequency projection, and bidirectional sequence modelling to produce the full complex S11 spectrum.The architecture is designed around geometric features in the pixel pattern and inter-frequency correlations.
  • Imbalance handling: Resonant samples are drawn 4× more frequently during training using a weighted sampler to reduce class-imbalance effects.Random horizontal and vertical flips are also applied to the pixel patterns as data augmentation.

C. Convolutional Autoencoder

A convolutional autoencoder learns a compact latent representation of feasible pixelated antenna geometries. Its reconstruction loss combines binary cross-entropy with total-variation regularisation.

  • Purpose: The autoencoder is trained to learn a compact latent representation of feasible antenna geometries for structured inverse optimisation.This avoids searching directly over the full binary surface, which can produce disconnected or physically invalid patterns.
  • Encoder: The encoder compresses a 1×19×23 binary pattern through convolutional blocks into a 64-dimensional latent vector z.Stride-2 convolutions reduce the representation to a 128×5×6 feature map before latent projection.
  • Decoder: The decoder reconstructs antenna patterns using bilinear upsampling and convolution, outputting per-pixel logits.The logits are converted into reconstructed pixel patterns for the autoencoder objective.
  • Training: The autoencoder training loss combines binary cross-entropy with a total-variation regulariser.The model is trained with AdamW at lr=10^-3 for up to 150 epochs with early stopping at patience 15.

D. Latent-Space Inverse Optimiser

The inverse optimiser performs gradient descent in the autoencoder’s 64-dimensional latent space rather than directly over binary pixels. Decoder binarisation, connectivity projection, regularisation, ensemble passes, frequency shifts, and multi-start search constrain and diversify the optimisation.

  • Latent-space optimisation: The inverse design search optimises a 64-dimensional autoencoder latent vector instead of 437 binary pixel values.This reduces dimensionality and constrains candidate patterns to physically valid antenna geometries.
  • Objective: The target loss penalises in-band |S11| values above −11 dB and suppresses spurious resonances outside a ±1 GHz guard band.The optimisation uses a frozen autoencoder decoder and frozen forward surrogate, with regularisers for sparsity, variation, pixel area, and latent magnitude.
  • Physical constraints: Each decoder output is passed through a sigmoid, thresholded into a binary pattern, and projected to retain only the largest metal region connected to the feed.A straight-through estimator passes gradients through the discrete binarisation step.
  • Robustness: A K=4 dropout ensemble, cyclic frequency shifts of ±60 and ±120 bins, and multi-start latent initialisation improve optimisation robustness.Half of the initial latent vectors are seeded from encoded resonant training patterns, while the remainder are sampled from a standard normal distribution.

IV. RESULTS

The CNN-BiLSTM surrogate generalises across dataset splits while accurately predicting broadband and resonant S11 characteristics for inverse design.

  • 1.55 dB validation and test broadband MAE, and 2.74 dB validation and test broadband RMSE, were consistent across splits.These metrics were reported for the 10K dataset.
  • 52% of samples had a true |S11| minimum below −10 dB, defining the resonant subset for resonant metrics.The resonant subset was used to compute dip-related performance measures.
  • 0.72 GHz mean dip frequency MAE was achieved across the test set.The inverse optimiser favoured candidates whose surrogate predictions were most reliable.

B. Inverse Design Results

Four inverse-designed antennas were evaluated against CST simulations across target bands within 22–30 GHz. All satisfied the −10 dB design criterion, with close agreement in most cases.

  • Inverse Design Results: Four antenna patterns were generated, exported to CST, and evaluated against a success criterion of |S11| reaching −10 dB or below within each target band.The targets covered 26.5–27.5, 22–23, 27–28, and 25 GHz.
  • Inverse Design Results: 0.76 GHz frequency error and 5.5 dB depth error occurred for the 26.5–27.5 GHz target.The predicted and CST-simulated centre frequencies were 27.76 GHz and 27 GHz, respectively.
  • Inverse Design Results: 0.44 dB depth error was obtained for the 22–23 GHz target, with both centre frequencies at 22.7 GHz.The surrogate and CST responses showed close agreement in this case.
  • Inverse Design Results: 0.18 dB depth error was obtained for the 27–28 GHz target, with predicted and simulated centre frequencies of 27.38 GHz and 27.4 GHz.
  • Inverse Design Results: 1.4 dB depth error was obtained for the 25 GHz target, with predicted and simulated centre frequencies of 24.95 GHz and 25.12 GHz.
  • Inverse Design Results: Three designs had frequency errors below 0.2 GHz and depth errors below 1.5 dB, while all four achieved |S11| ≤−10 dB within their target bands.The first design had the larger 5.5 dB depth discrepancy.
  • Inverse Design Results: The generated patterns remained connected and feed-attached, maintaining a continuous electrical path to the feed during optimisation.Connectivity projection was applied at every optimisation step.

V. CONCLUSION AND FUTURE WORK

The paper presents an end-to-end surrogate-assisted pipeline for automatically designing pixelated mmWave patch antennas, while identifying hardware validation and broader objectives as future work.

  • Conclusion: The pipeline combines XGBoost dataset augmentation, a CNN-BiLSTM complex-S11 surrogate, and 64-dimensional latent-space inverse optimisation.It uses connectivity projection to generate feed-connected patterns satisfying a |S11| ≤−10 dB specification.
  • Conclusion: Approximately 40% to 52% resonant-design proportion was achieved across the combined ∼10,000-simulation dataset through classifier-guided augmentation.
  • Conclusion: Four inverse-designed geometries were validated against full-wave simulation, supporting automatic custom antenna design and configuration within the reported scope.
  • Future Work: Future work includes fabrication and measurement, adding radiation pattern, gain, and efficiency targets, and extending the framework to two-port bandpass filter synthesis.Fabrication measurements are intended to quantify the simulation-to-hardware gap under real fabrication tolerances.
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