J. Pieter Jacobs

Gaussian process antenna modeling using neighborhood-data-expanded training sets

A cost-effective enhancement to the training of Gaussian process regression (GPR) models of microwave antenna (and other) structures is presented. In particular, we investigate improving GPR accuracy by employing additional training points that may typically be generated through sensitivity analysis, entailing negligible computational cost compared to obtaining additional data through full-wave simulations. We demonstrate, using two examples, that significant reduction of the modeling error is possible even though the location of the additional training points is constrained to the vicinity of the original training locations.

Gaussian process modeling of aperture efficiency ripple in reflector antennas

This paper presents a low cost Gaussian process (GP) modeling technique for antenna responses that exhibit highly oscillatory behavior as a function of frequency. Using a judiciously constructed composite covariance function that is able to capture the quasi-periodic behavior of the responses, an accurate interpolant could be established with far fewer training points than would normally be considered necessary for representing the oscillatory behaviour. The specific example investigated here is the aperture efficiency response of an offset Gregorian reflector antenna system, which has previously been shown to possess an oscillatory response which is computationally expensive to model accurately. Initial results using the suggested method are promising, with accurate interpolants of the expected response generated using only a sparse set of randomly selected training data. Notably, predictions were accurate even in sections of the response that contained multiple contiguous cycles and no training points.

Rapid simulation-based design of covered planar microstrip patch antenna arrays by means of radiation response surrogates

A technique for rapid simulation-based design of planar antenna arrays is presented. The proposed approach is based on establishing a suitable correction of the analytical array factor model of the array of interest. The corrected array factor is utilized as a fast surrogate allowing us to find the optimum element spacing and phase excitations at low computational cost. The correction terms are iteratively refined to account for design-dependent discrepancies between the array factor model and the EM-simulated one. Our methodology is demonstrated through the design of a 10 GHz planar 10-by-10 array of microstrip patch antennas with a plastic cover.

Low-cost design optimization of slot antennas using Bayesian support vector regression and space mapping

A computationally efficient procedure for design optimization of slot antennas is presented. We use space mapping as the main optimization engine, the underlying coarse model being coarse-discretization electromagnetic (EM) simulation data of the antenna structure of interest (low-fidelity model). In order to speed up the design process, the low-fidelity model is not used directly in the process; instead, the coarse-discretization simulation data - sampled only in the vicinity of their approximate optimum - are used to create an auxiliary response surface model through Bayesian support vector regression. The latter - after suitable space-mapping-based correction - serves as a prediction tool to find an accurate optimum design of the antenna. The proposed procedure is illustrated using two examples of slot antennas.

Two-Stage Gaussian Process Modeling of Microwave Structures for Design Optimization

Accurate models that can be rapidly evaluated are indispensable in microwave engineering. Kernel-based machine learning methods applied to the modeling of microwave structures have recently attracted attention; these include support vector regression, Bayesian support vector regression, and Gaussian process regression (GPR). In this chapter, we apply an extended methodology based on GPR, namely two-stage GPR, to the modeling of microwave antennas and filters. At the core of the method lies variable-fidelity electromagnetic simulations. In the first stage, a mapping between electromagnetic models (simulations) of low and high fidelity is learned, which allows for significantly reducing the computational effort necessary to set up the high-fidelity training data sets for the actual surrogate models (second stage), with negligible loss in predictive power. We apply the two-stage models to design optimization involving several examples of antennas and microstrip filters.

Bayesian Support Vector Regression Modeling of Microwave Structures for Design Applications

Fast and accurate models are indispensable in contemporary microwave engineering. Kernel-based machine learning methods applied to the modeling of microwave structures have recently attracted substantial attention; these include support vector regression and Gaussian process regression. Among them, Bayesian support vector regression (BSVR) with automatic relevance determination (ARD) proved to perform particularly well when modeling input characteristics of microwave devices. In this chapter, we apply BSVR to the modeling of microwave antennas and filters. Moreover, we discuss a more efficient version of BSVR-based modeling exploiting variable-fidelity electromagnetic (EM) simulations, where coarse-discretization EM simulation data is used to find a reduced number of fine-discretization training points for establishing a high-fidelity BSVR model of the device of interest. We apply the BSVR models to design optimization. In particular, embedding the BSVR model obtained from coarse-discretization EM data into a surrogate-based optimization framework exploiting space mapping allows us to yield an optimized design at a low computational cost corresponding to a few evaluations of the high-fidelity EM model of the considered device. The presented techniques are illustrated using several examples of antennas and microstrip filters.

Reduced-cost Bayesian support vector regression modeling and optimization of planar slot antennas

Bayesian support vector regression (BSVR) modeling of coplanar waveguide-fed slot antennas with reduced training sets for computational efficiency is presented. Coarse-discretization electromagnetic (EM) simulations are exploited in order to find a reduced number of training points used to establish a high-fidelity BSVR model of the antenna. As demonstrated using two antenna examples, the proposed technique allows substantial reduction (up to 48%) of the computational effort necessary to set up the high-fidelity models as compared to conventional approximation-based models, with negligible loss in accuracy. Application of the reduced BSVR models to antenna design is demonstrated.

Efficient Gaussian process modelling and optimization of slot antennas using a multi-fidelity approach for training data reduction

A methodology for reducing the computational cost of setting up Gaussian process (GP) models of coplanar waveguide (CPW)-fed slot antennas is presented. Our approach exploits finite-element frequency-domain simulations of different mesh densities with the coarse-mesh simulations used to find a reduced number of fine-mesh-simulated training points, eventually utilized to construct the GP surrogate model of the antenna. The surrogate is successfully applied to optimize the geometry parameters of the antenna within the adaptively-adjusted design specifications framework, even when the training data was reduced by as much as 70%. In the latter case, the computational cost of setting up the surrogate was only 40% of that of setting up a surrogate model using the full training data, while the total optimization time could be reduced by a third.