Editorial for the special issue on advances in forward and inverse surrogate modeling for high‐frequency design

Abstract

The design of modern-day high-frequency devices and circuits, including microwave/RF, antenna and photonic components, historically has relied on full-wave electromagnetic (EM) simulation tools. Initially used for design verification, EM simulations are nowadays used in the design process itself, for example, for finding optimum values of geometry and/or material parameters of the structures of interest. In a growing number of cases, EM-driven design closure is mandatory because alternative ways of evaluating the circuit performance (such as through equivalent network modeling) are grossly inaccurate and unable to account for cross-coupling effects (eg, in densely arranged layouts of compact circuits or antenna arrays), or various environmental components that affect the circuit performance (eg, connectors or housing for antenna structures). Despite being imperative, simulation-based design poses significant challenges, mostly due to the high computational cost of accurate, high-fidelity analysis. Repetitive simulations entailed by conventional optimization routines and even more by uncertainty quantification procedures (eg, Monte Carlo analysis) or tolerance-aware design tasks may generate the costs that are unmanageable or at least impractical. The availability of massive computational resources does not always translate into design speedup due to the need to account for interactions between devices and their surroundings as well as multiphysics (eg, EM-thermal) effects. Not surprisingly, traditional design procedures that directly utilize EM-simulated responses often fail or are impractical. Alternatives to full-wave simulation tools, therefore, are increasingly popular among EM designers. Among the many available options, fast surrogate models that accurately capture the electrical characteristics of the components of interest, recently have received significant attention. Replacing or supplementing EM analysis by the surrogates enables execution of simulation-based design tasks at low computational cost. This is especially the case for data-driven (approximation) models, which are by far the most popular ones due to their versatility and widespread availability. Some broadly used methods include polynomial regression, kriging, radial basis function, neural networks, and polynomial chaos expansion. The practical issue here is nonlinearity of high-frequency component outputs, which along with the curse of dimensionality, hinders utilization of this class of techniques for multiparameter components. Physics-based surrogates (eg, space mapping or various response correction methods) feature improved generalization capability at the expense of being problem specific: rendering the surrogate normally involves an underlying low-fidelity model, for example, equivalent network or coarse-mesh EM simulation. In addition to that, inverse modeling has been recently fostered as a practical alternative to forward models when solving certain types of design tasks, especially dimension scaling or high-frequency structures. The new developments concerning the improvements and generalizations of the existing methods as well as addressing dimensionality and scalability issues are under way. This special issue focuses on the current state of the art and future directions in forward and inverse surrogate modeling for high-frequency design. The issue contains 13 articles covering various aspects of numerical modeling of microwave and antenna components as well as design applications. Some of these articles are review works that give an account for the recent developments of particular methodologies. The largest number of articles is devoted to forward surrogate modeling methods in the context of specific design problems. In particular, Feng et al1 overview the advancements of parametric modeling of microwave components using neural networks with the system output represented by the zeros and poles of its corresponding transfer function. Koziel and Pietrenko-Dabrowska2 describe the developments of performance-driven surrogate modeling methods, which is one of the approaches recently proposed to address the dimensionality and parameter range issues in high-frequency modeling. Loukreziz et al3 propose a novel algorithm for sparse least squares-based polynomial chaos expansion models involving sequential experimental designs, whereas Georg and Römer4 discuss the utilization of conformal maps to construct basis functions for generalized polynomial chaos (gPC) as a way of enhancing its convergence properties. The advantages of the method are demonstrated using optical components. De Ridder et al5 address statistical modeling of frequency responses using linear Bayesian vector fitting. Finally, Hassan et al6 present computationally efficient microwave design centering using space mapping and a trust-region framework. A common theme of the aforementioned articles is to reduce the computational cost of EM-simulation-driven design processes, which is important from practical perspective, especially carrying out design closure in acceptable timeframes as well as design automation. The second group of articles in this special issue is focused on inverse modeling techniques. The work by Jin et al7 summarizes the recent developments in neural network-based inverse modeling for microwave design applications, whereas Koziel and Bekasiewicz8 discuss inverse surrogates for rapid dimension scaling of multiband antennas. Both works emphasize the fundamental advantages of inverse surrogates, that is, their capability of directly yielding near-to-optimum parameter sets corresponding to given performance requirements without the necessity of formal optimization. The third group of articles addresses application of surrogate modeling methods for the design of microwave/RF and antenna components. Xhafa and Yelten9 apply neural network models for variability analysis of low-noise amplifier, whereas Leifsson et al10 employ polynomial chaos-based kriging for uncertainty quantification of multiband patch antennas. The special issue is concluded with the articles by Belen et al11 and Mahouti et al12 which discuss design of 3D printed ceramic reflectarrays using neural network surrogates. As Guest Editors we would like to express our gratitude to Prof. Jianming Jin (Editor-in-Chief of Int J Numer Model) for the opportunity to publish this special issue. We would also like to thank all authors for their high-quality contributions, as well as all reviewers who devoted their time and expertise to careful review of the submissions. We do believe that the journal readers will find the presented works useful and that the special issue will help raising the awareness and popularity of surrogate modeling techniques as viable methodologies to enable expedited EM-driven design of high-frequency structures.