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.

Abstract-A methodology based on Gaussian process regression (GPR) for accurately modeling the resonant frequencies of dual-band microstrip antennas is presented. Two kinds of dual-band antennas were considered, namely a U-slot patch and a patch with a center square slot. Predictive results of high accuracy were achieved (normalized root-mean-square errors of below 0.6% in all cases), even for the square-slot patch modeling problem where all antenna dimensions and parameters were allowed to vary, resulting in a seven-dimensional input space. Training data requirements for achieving these accuracies were relatively modest. Furthermore, the automatic relevance determination property of GPR provided (at no additional cost) a mechanism for enhancing qualitative understanding of the antennas' resonance characteristics-a facility not offered by neural network-based strategies used in related studies.

Abstract-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 ) 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 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.

A procedure is presented for characterising the effects of varying finite substrate/ground plane size on the gain properties of microstrip antennas by means of Gaussian process regression (GPR). Two kinds of microstrip antenna were considered, namely a probe-fed patch antenna on both thin and thick dielectric substrates, and an L-probe-fed patch on a thick air substrate. CST Microwave Studio was used to generate training and test data for the GPR models. Frontal E and Hplane gain patterns could be predicted with normalised root-mean-square errors (RMSEs) of <1.8% for the thin-substrate probe-fed patch and the L-probe-fed patch; for the thick-substrate probe-fed patch, RMSEs were 2.1 and 2.8% for the two principal plane gain patterns, respectively. Furthermore, the GPR models could predict patterns at least two orders of magnitude faster than it took to obtain them via direct simulation in CST. Such models are expected to be useful in CAD-based environments for rapidly obtaining estimates of substrate/ground-plane size effects on gain characteristics in lieu of time-consuming full-wave simulations.

Abstract-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 S 11 against frequency of a CPW-fed secondresonant 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 S 11 / 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 benefits, including the need to learn only a handful of (hyper) parameters, and training errors that are effectively 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.