Recent Advances in High Frequency Modeling by Means of Domain Confinement and Nested Kriging

Development of modern high-frequency components and circuits is heavily based on full-wave electromagnetic (EM) simulation tools. Some phenomena, although important from the point of view of the system performance, e.g., EM cross-coupling effects, feed radiation in antenna arrays, substrate anisotropy, cannot be adequately accounted for using simpler means such as equivalent network representations. Consequently, the involvement of EM analysis, especially for tuning of geometry parameters, has become imperative in high-frequency electronics. Notwithstanding, excessive computational costs associated with massive full-wave simulations required by these procedures and even more by tasks such as uncertainty quantification or multi-criterial optimization, constitute a practical bottleneck. Repetitive evaluations of a structure can be facilitated by the use of fast replacement models (surrogates). Among available methods, approximation models are by far the most popular due to their flexibility and accessibility. Unfortunately, surrogate modeling of high-frequency structures is hindered by the curse of dimensionality and nonlinearity of system responses, primarily frequency characteristics. The recently proposed performance-driven techniques attempt to address this issue by appropriate confinement of the model domain to focus the modeling process only on the relevant part of the parameter space, i.e., containing the designs that are of high quality from the point of view the assumed performance figures. The nested kriging framework is perhaps the most advanced of these methods and allows for constructing reliable surrogates over broad ranges of the system parameters and operating conditions. This article summarizes the recent developments of the technique, including the basic formulation and several advancements aiming at the improvement of the surrogate predictive power or lowering the computational cost of training data acquisition. These include the incorporation of sensitivity data, as well as dimensionality reduction through principal component analysis. The problem of uniform data sampling in confined domains is also discussed. Our considerations are comprehensively illustrated using several examples of antennas and microwave circuits.