Table 5 Antenna III: modeling results and benchmarking.

Modeling method	Number of training samples^e
Modeling method	50	100	200	400	800
Kriging
Modeling error	61.4%	50.7%	39.8%	32.8%	31.8%
Model setup cost^b	50	100	200	400	800
RBF
Modeling error	65.3%	51.8%	43.2%	37.1%	33.6%
Model setup cost^b	50	100	200	400	800
Nested kriging⁶⁸
Modeling error	17.9%	13.3%	7.5%	5.4%	4.5%
Model setup cost^a	1949	1999	2099	2299	2699
No-reference-design modeling⁷³
Modeling error	10.8%	8.4%	7.1%	5.9%	5.0%
Model setup cost^c	242	292	392	592	992
Two-stage variable-resolution surrogate (this work)
N_Bf = 50
Modeling error	8.7%	7.2%	6.7%	6.5%	6.0%
Model setup cost^d	118.5	131.9	158.5	211.9	318.5
N_Bf = 100
Modeling error	6.8%	6.1%	5.4%	5.3%	5.2%
Model setup cost^d	168.5	181.9	208.5	261.9	368.5

^aThe cost includes acquisition of the reference designs, which is 1899 EM high-fidelity simulations of the antenna.
^bThe cost refers to high-fidelity simulations.
^cThe cost includes generation of random trial points, here, 192 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, 207 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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