Modified Multifidelity Surrogate Model Based on Radial Basis Function with Adaptive Scale Factor

Liu, Yin; Wang, Shuo; Zhou, Qi; Lv, Liye; Sun, Wei; Song, Xueguan

doi:10.1186/s10033-022-00742-z

Chinese Journal of Mechanical Engineering

Table 2 Statistical values of modeling capabilities of four test functions

From: Modified Multifidelity Surrogate Model Based on Radial Basis Function with Adaptive Scale Factor

		Test function
		Forretal function				Branin function				Beale function				Goldpr function
Sample size	Accuracy	MMFS	MFS-MFS	CO-RBF	RBF	MMFS	MFS-MFS	CO-RBF	RBF	MMFS	MFS-MFS	CO-RBF	RBF	MMFS	MFS-MFS	CO-RBF	RBF
4n	Average	0.5376	0.7665	0.0807	− 1.5439	0.9567	0.9099	0.6892	− 0.0658	0.3773	0.4880	0.0473	− 0.7525	0.3782	0.1595	0.2795	0.0188
	Median	0.8513	0.9932	0.3457	− 0.5454	0.9685	0.9512	0.7395	0.0348	0.4952	0.5766	0.0795	− 0.3666	0.3372	0.2195	0.2903	0.0393
	Variance	0.5492	0.2418	0.4709	4.1134	0.0012	0.0114	0.0235	0.5755	0.5125	0.0862	0.0415	2.2169	0.0508	0.1662	0.0608	0.1512
5n	Average	0.8666	0.9988	0.5310	− 0.7363	0.9612	0.9431	0.7258	0.0547	− 0.0519	0.4676	0.1596	− 0.7327	0.5380	0.3247	0.4602	0.0145
	Median	0.9242	0.9989	0.7316	− 0.3747	0.9700	0.9479	0.7688	0.1349	0.6368	0.5647	0.1873	− 0.1721	0.5523	0.4278	0.4675	0.1383
	Variance	0.0271	0.0000	0.2186	2.9783	0.0020	0.0006	0.0176	0.2854	4.1776	0.1128	0.0353	2.1298	0.0495	0.2325	0.0517	0.2495
6n	Average	0.9909	0.9989	0.9328	− 2.5924	0.9693	0.9451	0.7673	0.3026	0.5018	0.2937	0.0577	− 0.8134	0.5948	0.5290	0.5034	0.2344
	Median	0.9993	0.9992	0.9666	− 0.0993	0.9751	0.9716	0.8220	0.3822	0.5696	0.5533	0.1956	− 0.2666	0.6934	0.5788	0.5669	0.1826
	Variance	0.0005	0.0000	0.0067	92.9390	0.0004	0.0027	0.0178	0.3403	0.0901	0.8533	0.2031	2.8775	0.0463	0.0515	0.0477	0.1033
7n	Average	0.9897	0.9987	0.9491	0.4000	0.9717	0.9551	0.7665	0.3063	0.2693	0.5353	0.2604	− 0.0899	0.6301	0.5895	0.5326	0.4686
	Median	0.9995	0.9990	0.9793	0.5866	0.9764	0.9662	0.7834	0.3953	0.6228	0.5959	0.3358	− 0.0326	0.7369	0.6780	0.6075	0.4822
	Variance	0.0005	0.0000	0.0074	0.7013	0.0004	0.0011	0.0205	0.0935	0.8426	0.1202	0.0468	0.3814	0.0679	0.0522	0.0697	0.0932
8n	Average	0.9947	0.9994	0.9851	− 0.5568	0.9666	0.9472	0.7785	0.4096	0.4928	0.5373	0.3045	− 0.6113	0.6956	0.6388	0.5832	0.4184
	Median	0.9995	0.9996	0.9889	0.4147	0.9699	0.9568	0.8177	0.3578	0.6473	0.5760	0.2709	− 0.3205	0.7120	0.6794	0.5975	0.3078
	Variance	0.0002	0.0000	0.0003	9.2191	0.0003	0.0011	0.0238	0.1133	0.1265	0.0657	0.0253	1.6372	0.0210	0.0379	0.0439	0.0769
9n	Average	0.9999	0.9994	0.9938	0.7296	0.9696	0.9539	0.8477	0.3353	0.4784	0.5392	0.3126	− 0.4633	0.7954	0.7570	0.7184	0.6770
	Median	1.0000	0.9995	0.9945	0.8804	0.9771	0.9638	0.8844	0.4134	0.7295	0.6454	0.3377	− 0.1947	0.8078	0.7908	0.7162	0.7541
	Variance	0.0000	0.0000	0.0000	0.1187	0.0005	0.0009	0.0066	0.0972	0.5406	0.1083	0.0266	2.2869	0.0117	0.0132	0.0152	0.0530
10n	Average	0.9999	0.9996	0.9967	0.0518	0.9616	0.9419	0.8693	0.3283	0.5928	0.6275	0.3750	− 0.1812	0.8332	0.8040	0.7778	0.4189
	Median	1.0000	0.9998	0.9972	0.9425	0.9741	0.9676	0.9153	0.2906	0.7322	0.6890	0.4146	− 0.1163	0.8617	0.8412	0.8016	0.4905
	Variance	0.0000	0.0000	0.0000	10.5030	0.0009	0.0030	0.0084	0.0958	0.3833	0.0253	0.0325	0.1475	0.0091	0.0142	0.0157	0.1839

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