Spectral Bayesian Optimization Using a Physics-Informed Rational Szegö Kernel for Microwave Design

Microwave device design increasingly relies on surrogate modeling to accelerate optimization and reduce costly electromagnetic (EM) simulations. This paper presents a spectral Bayesian optimization (SBO) framework leveraging a physics-informed Gaussian process (GP) with a rational complex-valued Szegö kernel and input warping to enhance surrogate accuracy and data efficiency. Unlike conventional methods that model scalar objectives, our approach directly learns the complex-valued frequency response, enforcing causality and Hermitian symmetry. Effectiveness is demonstrated in two cases: a zig-zag microstrip bandpass filter optimized for magnitude response, and a passive differential equalizer optimized for both transmission magnitude and group delay. By embedding prior physics and modeling directly in the frequency domain, the method enables accurate, sample-efficient optimization of frequency-dependent behavior. This work shows how physics-informed Bayesian optimization can significantly improve microwave device design efficiency.