Variable-fidelity modeling of antenna input characteristics using domain confinement and two-stage Gaussian process regression surrogates

The major bottleneck of electromagnetic (EM)-driven antenna design is the high CPU cost of massive simulations required by parametric optimization, uncertainty quantification, or robust design procedures. Fast surrogate models may be employed to mitigate this issue to a certain extent. Unfortunately, the curse of dimensionality is a serious limiting factor, hindering the construction of conventional data-driven models valid over wide ranges of the antenna parameters and operating conditions. This paper proposes a novel surrogate modeling approach that capitalizes on two recently proposed frameworks: the nested kriging approach and two-stage Gaussian process regression (GPR). In our methodology, the first-level surrogate, of nested kriging, is applied to define the confined domain of the model in which the final surrogate is constructed using two-stage GPR. The latter permits blending information from a sparsely sampled high-fidelity EM simulation model and a densely sampled low-fidelity (or coarse-mesh) model. This combination enables significant computational savings in terms of training data acquisition while retaining excellent predictive power of the surrogate. At the same time, the proposed framework inherits all the benefits of nested kriging, including ease of uniform sampling of the confined domain, as well as straightforward generation of a good initial design for surrogate model optimization. Comprehensive benchmarking carried out using two antenna examples demonstrates superiority of our technique over conventional surrogates (unconfined domain), and standard GPR applied to the confined domain. Application examples for antenna optimization are also provided.