Abstract
Fast replacement models (or surrogates) have been widely applied in the recent years to accelerate simulation-driven design procedures in microwave engineering. The fundamental reason is a considerable—and often prohibitive—CPU cost of massive full-wave electromagnetic (EM) analyses related to solving common tasks such as parametric optimization or uncertainty quantification. The most popular class of surrogates are data-driven models, which are fast to evaluate, versatile, and easy to handle. Notwithstanding, the curse of dimensionality as well as the utility demands (e.g., so that the model covers sufficiently broad ranges of the system operating conditions), limit the applicability of conventional methods. A performance-driven modeling paradigm allows for mitigating these issue by focusing the surrogate setup process in a constrained domain encapsulating designs being of high quality w.r.t. the assumed figures of interest. The nested kriging framework capitalizing on this idea, renders the constrained surrogate using kriging interpolation, and has been shown to surpass traditional approaches. In pursuit of further accuracy improvements, this work incorporates the performance-driven concept into the fully-connected regression model (FRCM). The latter has been recently introduced in the context of frequency selective surfaces, and combined deep neural networks with Bayesian optimization, the latter employed to determine the network architecture and hyper-parameters. Using two examples of miniaturized microstrip couplers, our methodology is demonstrated to outperform both conventional modeling techniques and nested kriging, with reliable models constructed over multi-dimensional parameters spaces using just a few hundreds of samples.
Highlights
Contemporary microwave design is a challenging task, where the strive to meet stringent performance specifications is compromised by the necessity of satisfying various constraints related to device cost or its physical dimensions [1], [2]
The results are consistent for both the rat-race coupler (RRC) and branch-line coupler (BLC), which demonstrates that the considered method can handle various modeling problems without any tuning of its control parameters
It allows us to take the advantage of the neural network flexibility in modeling of highly-nonlinear responses while avoiding the risk of overtraining, and to adjust the structure of the model to a specific input data set
Summary
Contemporary microwave design is a challenging task, where the strive to meet stringent performance specifications is compromised by the necessity of satisfying various constraints related to device cost or its physical dimensions [1], [2]. A recent example if a fully-connected regression model (FCRM) [42], where all components of the DNN, including its architecture, are adjusted through Bayesian optimization (BO) [43]. Another possibility is ensemble learning (EL) [44], where individual models (referred to as learners) are combined as building blocks of a more involved surrogate [45]. 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]. It should be emphasized that the FCRM architecture can be automatically adjusted to the specific input data so that no user interaction/expert knowledge needs to be engaged [42]
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