Modeling Microwave S-parameters using Frequency-scaled Rational Gaussian Process Kernels

This work presents a machine learning technique to model the complex-valued scattering parameters (S-parameters) of passive microwave devices as a function of frequency and a set of design variables. The proposed Gaussian process (GP) model intricately models the real and imaginary parts of the S-parameters by employing a physics-informed kernel, adept at representing complex holomorphic functions and incorporating the Hermitian symmetry inherent in scattering parameters. Additionally, to extend the kernel's capabilities to higher dimensions beyond standard GP techniques, it is extended with a frequency scaling, enhancing the modeling capacity. The resulting physics-informed frequency-scaled GP model accurately predicts the S-parameter values at desired parameter configurations in the design space. One application example demonstrates the superiority of the new kernel, compared to standard GP kernels.