KARMA: Kernel-Aided Rational Macromodeling of Noisy Electrical Frequency Response Data

Gaussian processes (GPs) have attracted significant interest for macromodeling frequency-domain responses of linear time-invariant (LTI) systems. Yet, a unified and practical approach to extend their use to the time domain has remained elusive. This article introduces kernel-aided rational macromodeling (KARMA), a novel framework that constructs compact, multiport rational representations suitable for circuit simulation directly from frequency response data. By leveraging the unique properties of complex-valued rational kernels, KARMA fuses the advantages of kernel-based nonparametric methods with the physical properties of traditional rational parametric macromodeling techniques. The framework comprises critical components such as joint hyperparameter optimization, passivity enforcement, and model order reduction (MOR). Moreover, the probabilistic nature of GPs enables KARMA to generate uncertainty-aware macromodels, making the framework particularly effective in noisy or data-scarce settings.