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Accelerating Antenna Design Exploration with Neural Network Surrogate Models: A COMSOL Multiphysics-Based Workflow

This article outlines a COMSOL-to-surrogate workflow for antenna design, enabling millisecond prediction, fast optimization, and collaborative tradeoff exploration.

Abstract

Modern antenna development often involves balancing electrical performance, manufacturability, material constraints, cost and thermal management. Rigorous full-wave simulation of parameterized antenna geometries can be computationally intensive, given the fact there can be up to a dozen geometrical parameters, making design exploration and antenna performance studies difficult. PhysAI has developed a workflow using COMSOL Multiphysics to generate high-fidelity surrogate models that learn the mapping between geometric design parameters and antenna S-parameters over a set frequency range. Once trained, these neural-network-based surrogate models evaluate in milliseconds, enabling real-time design iteration and interactive performance visualization.

This approach allows product managers and RF engineers to jointly explore the design space, assess tradeoffs, and identify solutions that balance performance with practical constraints, rather than relying solely on global optimization. Designs which offer near-optimal performance, but improved manufacturability become easier to identify, and robustness analyses can be performed rapidly by sampling around nominal solutions. A real-world antenna test case is studied in the field of RFID tag localization, where antenna impedance matching, gain and far-field pattern are crucial to overall performance. The workflow demonstrates how surrogate modeling accelerates early-stage design and reduces the number of full numerical simulations required. The outcome is a faster, more transparent antenna development process, one where performance and product constraints can be balanced dynamically as opposed to being discovered late in the design cycle.

Introduction

Antennas are fundamental components in wireless communication systems, ranging from mobile devices and IoT sensors to satellite communications and radar systems. As wireless technologies advance, particularly with the proliferation of 5G/6G networks, RFID systems, and autonomous vehicles, the demands on antenna performance have intensified. Modern antennas must deliver high gain, wide bandwidth, specific radiation patterns, and efficient impedance matching while adhering to strict constraints on size, cost, materials, manufacturability, and thermal dissipation.

Traditional antenna design relies heavily on full-wave electromagnetic (EM) solvers such as COMSOL Multiphysics, ANSYS HFSS, or CST Microwave Studio. These tools provide high-fidelity predictions of antenna behavior through finite element method (FEM), method of moments (MoM), or finite-difference time-domain (FDTD) techniques. However, each simulation can take minutes to hours, depending on geometry complexity and frequency resolution. When optimizing or exploring designs with 10–15 geometric parameters (e.g., patch dimensions, feed positions, substrate thickness, slot lengths), the computational burden becomes prohibitive. A large parametric sweep might require thousands of simulations, consuming days or weeks of compute time.

This bottleneck limits early-stage design exploration, where engineers and product stakeholders need to evaluate trade-offs collaboratively. Global optimization algorithms can identify theoretical optima, but they often yield designs that are difficult to manufacture or sensitive to tolerances. Late discovery of these practical issues leads to costly iterations.

Machine learning-based surrogate models offer a powerful solution. By training neural networks on data from a manageable number of high-fidelity simulations, surrogates can approximate EM responses in milliseconds. This enables interactive exploration, rapid sensitivity analysis, and multi-objective trade-off visualization.

PhysAI has developed an end-to-end workflow leveraging COMSOL Multiphysics for training data generation and neural networks for surrogate modeling. The following sections describe the approach, workflow details, and a practical case study in RFID tag localization.

Challenges in Contemporary Antenna Design

Antenna design is inherently multi-objective. Key electrical metrics include:

These must be balanced against practical constraints:

In traditional workflows, RF engineers perform iterative simulations, often guided by experience or single-objective optimization. Product managers enter later, assessing feasibility only after significant design investment. This sequential process risks "perfect" designs that fail in production.

Surrogate Modeling Approach

Surrogate models approximate expensive simulations using data-driven techniques. In EM design, neural networks excel at learning complex mappings from geometric parameters to frequency-dependent outputs like S-parameters.

The PhysAI workflow uses fully connected deep neural networks (DNNs) trained on S-parameter values across a frequency range. Inputs are normalized geometric parameters or material properties; outputs are vectorized S-parameter responses. This formulation captures broadband behavior accurately.

Once trained, the surrogate enables:

Detailed Workflow

The workflow comprises six phases:

  1. Parameterization Determination and Sampling: Define geometric parameters and bounds based on requirements and constraints. Use Latin Hypercube Sampling (LHS) to generate 200–1000 designs efficiently covering the space.
  2. Physics Model: Set up a detailed 3D physics model of the electromagnetic wave propagation in COMSOL and test some nominal cases.
  3. High-Fidelity Data Generation. Run batch COMSOL simulations using the Surrogate Model Training study type. Extract S-parameters (and if needed, far-field patterns, and derived metrics such as gain or efficiency).
  4. Surrogate Training: Preprocess data (normalize, split train/validation). Train the deep neural network with architectures like 3-4 hidden layers and 32-64 neurons. Use mean-squared error loss.
  5. Deployment and Exploration: Integrate surrogate into a dedicated app using the COMSOL Application Builder. The user has the option to explore the parameter spaces manually using sliders or optimize the design using only inference on the surrogate model.
  6. Validate the chosen design configuration by re-running the full FEA model at the chosen set of conditions.

This reduces full simulation time by 95%+, reserving them for final verification.

Figure 1: Overview of the surrogate-assisted antenna design workflow, integrating high-fidelity simulation, machine learning, and interactive exploration.

Case Study: RFID Tag Localization Antenna

RFID tag localization systems require tag antennas with precise impedance matching, moderate gain, and controlled radiation patterns for accurate positioning in warehouses or retail environments. Operating at UHF (902–928 MHz in North America), these antennas must balance read range, multipath rejection, and cost-effective fabrication.

A parameterized meandered-line dipole antenna on FR4 substrate with complex chip impedance was studied. Five geometric parameters are considered:

Key objective:

Other things can be optimized if needed, for example:

RFID tags contain a small chip which is used to activate the tag. Chip impedance is an important variable in tag design. In this example, the chip resistance Rc is 11.5 ohm and the capacitance Cc is 3 pF. Lower chip resistance tends to make matching more difficult. The goal is to design an antenna whose natural impedance is a conjugate match for the chip impedance. The complex chip impedance is:

Chip impedance equation from the source document.

so the antenna needs to have an inherent impedance:

Conjugate-matching impedance equation from the source document.

The S-parameter, the quantity we want to minimize close to the target frequency of 915MHz is given by:

S-parameter equation from the source document.

The basic layout of the tag is shown in Figure 2. The geometric features will be adjusted and optimized until the antenna meets the performance requirements. The S-parameter plot for these nominal initial values is shown in Figure 3. The initial design doesn’t meet the performance specification or have the correct resonant frequency.

Figure 2: Example geometry of a miniaturized single-port meandered-line dipole antenna suitable for RFID applications.

Figure 3: S-parameter vs. frequency for an arbitrary initial starting point. Both the resonance location and amplitude of the S-parameter need to be improved.

Using Latin Hypercube Sampling (LHS), 300 COMSOL frequency sweep simulations are performed (average 3 minutes each on a 32-core workstation, total ~15 hours). The 15-hour simulation time is chosen intentionally, as one can set the model solving at the end of the workday, and have the results available for processing the following morning.

Results and Interactive Exploration

Once the surrogate model has run, the data can be used to train a deep neural network. When trained, the result is a function which can be evaluated using frequency and the geometric inputs. The function form is thus:

Surrogate function expression from the source document.

where the first 5 inputs are the geometric parameters and fr is the range of frequencies over which to evaluate. Evaluation of this function for different combinations of parameters is practically instant, as a weighted sum (from the weights and biases computed during training) is evaluated under-the-hood.

The evaluation, result display and convenient method of changing input parameters (using a slider which updates the results and geometry plot in real-time) can be packaged into a simple and intuitive user interface using the COMSOL Application Builder. The app also has a “Verify Results” button in the ribbon. This allows the full FEA solution to be computed once an interesting result has been obtained. This is a crucial and necessary step when using this technique, the full model should always be computed for verification purposes.

Figure 4: Screenshot of the app which allows rapid tag design iteration using only inference on the neural network. A 5-dimensional geometric parameter space can be explored with millisecond evaluation of the S-parameters.

The interactive dashboard provided by the app allows cross-functional teams to filter designs by constraints (e.g., cost proxies via material volume) and select candidates for prototyping.

Optimization

Manual tuning of the parameters, while instructive, can be time consuming, even when just running inference from the surrogate model. Optimization running on inference can compute global minima for a suitable objective function. In this case, the S-parameter is minimized over a user selected frequency range. The objective function is thus:

Optimization objective equation from the source document.

The parameter space of antenna configurations can contain many local minima, but only one true global. COMSOL includes an EGO (efficient global optimization) solver which can compute a true global minimum. Running this for different objective functions can quickly generate a desirable starting point, which can be manually tweaked given the practical design issues discussed earlier.

The screenshot in Figure 4 shows a result which was first computed using the optimization, then tweaked slightly to get the minimum at exactly 915MHz. The frequency range in which to optimize is specified in the user interface. If a high bandwidth is required, the frequency limits can be expanded. If the main goal is to have the smallest S-parameter at exactly 915MHz, the window can be shrunk to a very small value. The user can quickly see the tradeoffs in geometrical footprint and performance given their target specification.

Figure 5: Optimized S11 plot for the antenna design, showing resonance frequency and bandwidths at -3, -5 and -10dB.

An added benefit to this approach is that derivatives of the objective function can be computed purely from the inference. This allows the sensitivity of the S-parameter with respect to each geometric parameter to be quantified. These values indicate which of the dimensions will affect performance the most if the exact values are not met during manufacturing. These can be explored further using uncertainty quantification, if needed.

The optimized result for a frequency range of 910 to 920 MHz is shown in Figure 5. The antenna meets the target of -20dB and the resonance is at exactly 915 MHz. Expanding the frequency integration range would result in slightly different solutions, with the antenna obtaining a higher bandwidth, but the frequency at which the S-parameter is minimized might be slightly away from 915 MHz.

Note: Running optimization on the full FEA model would require an inordinate number of solutions to be computed, limiting runs to overnight or possibly over weekends. Crucially, if the objective function changes, the optimization needs to be re-run.

Discussion

This workflow shifts antenna design from simulation-constrained iteration to data-driven collaboration. Surrogates democratize access, enabling product managers to quantify trade-offs early. The simple RFID case demonstrates practical benefits: identifying manufacturable designs without sacrificing core performance.

Limitations include initial data generation cost (mitigated by cloud and batch compute) and surrogate validity only within training bounds.

Conclusion

Neural network surrogate models trained on COMSOL Multiphysics simulation data enhance and speed up antenna design and development. By enabling millisecond evaluations, this approach facilitates interactive exploration, rapid robustness analysis, and balanced decision-making across electrical and practical constraints. The RFID tag case study illustrates accelerated early-stage design with fewer full simulations required. As computational tools evolve, such hybrid simulation-ML workflows promise more innovative, reliable, and cost-effective antenna solutions. Running global optimization with different objective functions can be used in conjunction with manual adjustments, to ensure performance requirements are met, but manufacturing constraints and costs are also met. This technique is generally applicable to all types of physics using COMSOL Multiphysics, making it a powerful modeling tool for rapid design optimization.