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.