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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