J. P. Jacobs

GAUSSIAN PROCESS MODELING OF CPW-FED SLOT ANTENNAS

Gaussian process (GP) regression is proposed as a structured supervised learning alternative to neural networks for the modeling of CPW-fed slot antenna input characteristics. A Gaussian process is a stochastic process and entails the generalization of the Gaussian probability distribution to functions. Standard GP regression is applied to modeling S11 against frequency of a CPW-fed second- resonant slot dipole, while an approximate method for large datasets is applied to an ultrawideband (UWB) slot with U-shaped tuning stub | A challenging problem given the highly non-linear underlying function that maps tunable geometry variables and frequency to S11=input impedance. Predictions using large test data sets yielded results of an accuracy comparable to the target moment-method-based full-wave simulations, with normalized root mean squared errors of 0.50% for the slot dipole, and below 1.8% for the UWB antenna. The GP methodology has various inherent beneflts, including the need to learn only a handful of (hyper) parameters, and training errors that are efiectively zero for noise-free observations. GP regression would be eminently suitable for integration in antenna design algorithms as a fast substitute for computationally intensive full-wave analysis.

Bayesian Support Vector Regression With Automatic Relevance Determination Kernel for Modeling of Antenna Input Characteristics

The modeling of microwave antennas and devices typically requires that non-linear input-output mappings be determined between a set of variable parameters (such as geometry dimensions and frequency), and the corresponding scattering parameter(s). Support vector regression (SVR) employing an isotropic Gaussian kernel has been widely used for such tasks; this kernel has one tunable hyperparameter that can be optimized (along with the penalty constant C) using a standard procedure that involves a parameter grid search combined with cross-validation. The isotropic kernel however suffers from limited expressiveness, and might provide inadequate predictive accuracy for nonlinear mappings that involve multiple tunable input variables. The present study shows that Bayesian support vector regression using the inherently more flexible Gaussian kernel with automatic relevance determination (ARD) is eminently suitable for highly non-linear modeling tasks, such as the input reflection coefficient magnitude |S11| of broadband and ultrawideband antennas. The Bayesian framework enables efficient training of the multiple kernel ARD hyperparameters-a task that would be computationally infeasible for the grid search/cross-validation approach of standard SVR.

Two-Stage Framework for Efficient Gaussian Process Modeling of Antenna Input Characteristics

A two-stage approach based on Gaussian process regression that achieves significantly reduced requirements for computationally expensive high-fidelity training data is presented for the modeling of planar antenna input characteristics. Our method involves variable-fidelity electromagnetic simulations. In the first stage, a mapping between electromagnetic models (simulations) of low and high fidelity is learned, which allows us to substantially reduce (by 80% or more) 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 illustrate our method by modeling the input characteristics of three antenna structures with up to seven design variables. The accuracy of the two-stage method is confirmed by the successful use of the surrogates within a space-mapping-based optimization/design framework.

Computationally Efficient Multi-Fidelity Bayesian Support Vector Regression Modeling of Planar Antenna Input Characteristics

Bayesian support vector regression (BSVR) modeling of planar 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 fine-discretization training points for establishing a high-fidelity BSVR model of the antenna. As demonstrated using three planar antennas with different response types, the proposed technique allows substantial reduction (up to 48%) of the computational effort necessary to set up the fine-discretization training data sets for the high-fidelity models with negligible loss in predictive power. The accuracy of the reduced-data BSVR models is confirmed by their successful use within a space mapping optimization/design algorithm.

Low-profile CPW-fed slot antenna with parasitic slot on conductor-backed two-layer substrate

A previously reported design consisting of a CPW-fed slot antenna with a parasitic slot on a conductor-backed single-layer substrate is extended to an electrically thin, low-profile conductor-backed two-layer substrate. In doing so, several enhancements are effected, including relative insensitivity of main beam direction to slot dimensions, a non-leaky CPW-feed line, easier matching, and a gain that exceeds 11 dBi at the operating frequency. Low cross-polarization levels were also achieved.

On the modeling of non-stationary antenna responses by Gaussian processes

This paper describes the modeling of the complex reflection coefficient S11 of a meta-material antenna comprised of an etched microstrip dipole antenna radiating in the presence of a back reflector that is an artifical magnetic conductor (AMC). Both the real and imaginary components of the S parameter exhibit significant changes in rate of variation as a function of position along the frequency dimension of the input space. We show that Gaussian process regression — using a specially constructed composite covariance function that allows for a variable length-scale parameter along the frequency dimension — can succesfully model the components of S11. The latter model outperforms a GP model using a well-known standard covariance function from the (stationary) Matérn family.

Efficient Modeling of Missile RCS Magnitude Responses by Gaussian Processes

An efficient technique for modeling radar cross section magnitude responses versus frequency is presented. The technique is based on Gaussian process regression and makes it possible to significantly reduce the number of expensive computer simulations required to accurately resolve these responses. Examples of two missiles are used to evaluate the proposed technique. Average predictive normalized root-mean-square errors (RMSEs) of 1.24% and 1.63% were obtained, with the worst RMSE being less than 2.2%. These results were significantly better than results obtained with alternative techniques, including geometric theory of diffraction-based modeling and support vector regression.

Accurate modeling of wideband antennas using variable-fidelity simulations, kriging and parameterized response correction

A simple methodology for accurate modeling of wideband antennas is presented. Our approach exploits kriging interpolation of sampled coarse-discretization EM simulation data as an initial surrogate model. A parameterized response correction is subsequently used to improve this initial model with the correction coefficients obtained analytically, based on sparsely sampled high-fidelity EM simulations results of the antenna structure of interest. The resulting surrogate model is very fast, accurate, and, most importantly, it can be constructed at a low computational cost. The last feature makes is suitable for solving design tasks such as performance optimization. Our considerations are illustrated using an example of a broadband slot antenna.

Single-model versus ensemble-model strategies for efficient Gaussian process surrogate modeling of antenna input characteristics

Gaussian process regression has been shown to be a highly effective tool for modeling the input characteristics of antennas. This study presents, for the first time, a rigorous comparison of two strategies for modeling Re{S11}, Im{S11}, and |S11|: the standard single-model method, and an approach that employs an ensemble of independent single models, one per equally-spaced frequency value in the range of interest. In spite of the fact that it uses far less training data, the singlemodel technique for the most approximately matched or even outdid the ensemble of GPR models in predictive performance - this appears to be due to the fact that the ensemble model disregards important covariance information regarding the latent function associated with the frequency dimension.

Calculation of Mutual Admittance Between CPW-Fed Slots on Two-Layer Conductor-Backed Substrates Using Reciprocity-Based Expression

A computational strategy, based on a well-known reciprocity-based formulation, for finding the mutual admittance Y12 between CPW-fed slots on conductor-backed two-layer substrates is presented. Simplifying assumptions make it possible to determine Y12 against inter-slot spacing d by performing a once-only moment-method analysis of each slot in isolation, and then calculating external and internal reaction integrals at each value of d. It is shown that Y12 against d calculated for CPW-fed twin slots on conductor-backed two-layer substrates agrees well with simulations of the full twin-slot structure using the moment-method-based simulator IE3D.