Bayesian Optimization for Microwave Devices Using Deep GP Spectral Surrogate Models

In microwave design, Bayesian optimization (BO) techniques have been widely applied to the optimization of the frequency response of components and devices. The common approach in BO is to model and maximize an objective function over the design parameters, in order to find the optimal spectral response. Such an approach avoids the direct modeling of spectral responses, which is a challenging task for the typical data-efficient surrogate models used in BO. Simple objective functions may lead to a suboptimal solutions, while complicated objectives require more powerful and less data-efficient surrogate models. To resolve this issue, this article proposes to adopt a deep Gaussian process (DGP) to directly model all relevant $S$ coefficients over the frequency and the design parameter ranges of interest. Subsequently, an objective probability distribution is retrieved from the DGP model and maximized using a BO scheme. The proposed approach is tested on two suitable microwave examples and compared to the standard BO approach. Results show increased accuracy in identifying the optimal frequency response for the given design parameters and the desired objective, while maintaining high data efficiency.