Table 4 Antenna II: modeling results and benchmarking.

Modeling method	Number of training samples^e
Modeling method	50	100	200	400	800
Kriging
Modeling error	21.7%	17.3%	12.6%	9.3%	7.2%
Model setup cost^b	50	100	200	400	800
Modeling error	24.9%	19.8%	14.3%	10.5%	8.7%
RBF
Model setup cost^b	50	100	200	400	800
Modeling error	9.9%	6.4%	4.4%	3.8%	3.4%
Nested kriging⁶⁸
Model setup cost^a	980	1030	1130	1330	1730
Modeling error	7.3%	5.1%	3.8%	3.1%	2.5%
No-reference-design modeling⁷³
Model setup cost^c	280	330	430	630	1,030
Modeling error	5.4%	3.1%	2.5%	2.1%	1.7%
Two-stage variable-resolution surrogate (this work)
N_Bf = 50
Model setup cost^d	132.8	148.4	179.7	242.2	367.2
Modeling error	3.5%	3.0%	2.3%	1.8%	1.6%
N_Bf = 100
Model setup cost^d	182.8	198.4	229.7	292.2	417.2

^aThe cost includes acquisition of the reference designs, which is 930 EM high-fidelity simulations of the antenna when using feature-based optimization⁶⁷ as listed in the table. Conventional (minimax) optimization required 1201 high-fidelity simulations.
^bThe cost refers to high-fidelity simulations.
^cThe cost includes generation of random observables, here, 230 high-fidelity simulations in total to yield N_r = 50 accepted samples.
^dThe cost includes generation of random trial points at low-fidelity level, here, 215 simulations in total to yield N_r = 50 accepted samples.
^eIn the case of the proposed model, the numbers 50 through 800 refer to low-fidelity EM simulations.

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