Abstract
Utilization of fast surrogate models has become a viable alternative to direct handling of full-wave electromagnetic (EM) simulations in EM-driven design. Their purpose is to alleviate the difficulties related to high computational cost of multiple simulations required by the common numerical procedures such as parametric optimization or uncertainty quantification. Yet, conventional data-driven (or approximation) modeling techniques are severely affected by the curse of dimensionality. This is a serious limitation when it comes to modeling of highly nonlinear antenna characteristics. In practice, general-purpose surrogates can be rendered for the structures described by a few parameters within limited ranges thereof, which is grossly insufficient from the utility point of view. This paper proposes a novel modeling approach involving variable-fidelity EM simulations incorporated into the recently reported nested kriging modeling framework. Combining the information contained in the densely sampled low- and sparsely sampled high-fidelity models is realized using co-kriging. The resulting surrogate exhibits the predictive power comparable to the model constructed using exclusively high-fidelity data while offering significantly reduced setup cost. The advantages over conventional surrogates are pronounced even further. The presented modeling procedure is demonstrated using two antenna examples and further validated through the application case studies.
Highlights
Full-wave electromagnetic (EM) simulation has become the single most important tool in a practical design of contemporary antenna structures
This paper combines the latest of these developments, the performancedriven modeling within a constrained domain with the use of two-level kriging surrogates, with variable-fidelity EM simulation models to further reduce the computational cost of surrogate model construction
Co-kriging requires rendering of the two models: sKRc set up using the low-fidelity data (XBc, Rc(XBc)), and sKRf generated on the residuals (XBf, r), where r = Rf (XBf ) – ρ·Rc(XBf ), here, ρ is a part of the Maximum Likelihood Estimation (MLE) of the second model
Summary
Full-wave electromagnetic (EM) simulation has become the single most important tool in a practical design of contemporary antenna structures. Koziel: Antenna Modeling Using Variable-Fidelity EM Simulations and Constrained Co-Kriging surfaces [20], kriging [21], neural networks [22]), as well as machine learning techniques [23], [24]. This paper combines the latest of these developments, the performancedriven modeling within a constrained domain with the use of two-level kriging surrogates (i.e., the nested kriging technique of [41]), with variable-fidelity EM simulation models to further reduce the computational cost of surrogate model construction. Demonstration examples indicate superiority of the proposed method over both conventional models and single-fidelity nested kriging as well as a possibility of rendering design-ready surrogates at the cost corresponding to less than two hundred high-fidelity antenna simulations
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