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

Abstract

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 paper 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.

Data driven surrogate modeling of horn antennas for optimal determination of radiation pattern and size using deep learning

“…In this section, the proposed data-driven surrogate model-assisted design optimization of horn antenna will be presented in details. Here, Artificial Intelligence (AI) regression algorithms that had shown great potential in modeling of microwave components, 24,27,40,41 are taken into consideration to create a data-driven surrogate model (Figure 1E) to map the input variable space to the radiation pattern characteristics of the antenna. Multi-Layer Perceptron (MLP), Support Vector Regression Machine (SVRM), Gaussian Process Regression (GPR), and Ensemble Learning (EL), Modified Multi-Layer Perceptron (M2LP) 42 algorithms had been used for creating the surrogate model of the horn antenna that are trained with K = 4 K-fold validation and a holdout-data set with 25 samples (randomly selected in the defined range given in Table 1) is used for evaluation of over-fitting using Mean Absolute Error (MAE) metric using the predicted value by surrogates and the actual response from the 3D EM solver.…”

“…Data-driven surrogate modeling has proved its usage in the design procedure of highfrequency devices as a low-cost surrogate of the various electrical and field responses of high-frequency stages such as scattering parameters [S], 14,15 reflection phase characteristics in reflect-arrays, 16 characteristic impedance, 17 and prediction resonant frequency of antenna designs. [18][19][20] In each of the mentioned works, different types of Artificial Intelligence (AI) regression methods such as polynomial, 21,22 kriging, [23][24][25] Support Vector Regression (SVR), [26][27][28][29] Artificial Neural Networks (ANNs), [30][31][32][33][34] and Deep Learning (DL) [35][36][37][38][39] had been used to create an accurate, stable mapping between the given input space of the problem and the targeted characteristic as the output of the model.…”

Improved Modeling of Microwave Structures Using Performance-Driven Fully-Connected Regression Surrogate

“…The constrained domain of the surrogate model is determined using pre-optimized reference designs and an inverse regression model, whereas the final surrogate is constructed using kriging interpolation [48]. The domain confinement concept has been shown to significantly improve the modeling accuracy, and enabled reliable surrogate rendition over wide ranges of geometry parameters [49]. This paper proposes a novel approach to modeling of miniaturized microwave components.…”

“…This paper proposes a novel approach to modeling of miniaturized microwave components. Our methodology combines the fully-connected regression model [42] involving Bayesian optimization for automated determination of the underlying DNN architecture, and the concept of domain confinement as formulated in the nested kriging framework [49]. The employment of FCRM allows us to more efficiently handle nonlinear frequency characteristics of the microwave components as well as account for specific allocation of the training data (particularly crucial for smaller data sets).…”