Table 3 Antenna I: modeling results and benchmarking.

Modeling method	Number of training samples^e
Modeling method	50	100	200	400	800
Kriging
Modeling error	56.9%	50.8%	35.8%	31.5%	25.6%
Model setup cost^b	50	100	200	400	800
Modeling error	61.0%	53.2%	37.9%	34.1%	27.2%
RBF
Model setup cost^b	50	100	200	400	800
Modeling error	19.4%	12.9%	7.7%	5.1%	3.7%
Nested kriging⁶⁸
Model setup cost^a	914	964	1064	1264	1664
Modeling error	13.4%	9.9%	6.9%	5.4%	4.4%
No-reference-design modeling⁷³
Model setup cost^c	156	206	306	506	906
Modeling error	13.1%	8.5%	6.7%	5.1%	4.3%
Two-stage variable-resolution surrogate (this work)
N_Bf = 50
Model setup cost^d	106.7	123.3	156.7	223.3	356.7
Modeling error	8.2%	7.7%	5.3%	4.2%	3.5%
N_Bf = 100
Model setup cost^d	156.7	173.3	206.7	273.3	406.7

^aThe cost includes acquisition of the reference designs, which is 864 EM high-fidelity simulations of the antenna when using feature-based optimization⁶⁷ as listed in the table. Conventional (minimax) optimization required high-fidelity 1012 simulations.
^bThe cost refers to high-fidelity simulations.
^cThe cost includes generation of random trial points, here, 106 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, 120 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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