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Table 1 Basis functions of RBF

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

Basis function name

Basis function form

Basis function name

Basis function form

Linear

\(\varphi \left(r\right)=r\)

Gaussian

\(\varphi \left(r\right)={e}^{-{r}^{2}/2{\sigma }^{2}}\)

Cubic

\(\varphi \left(r\right)={r}^{3}\)

Multiquadric

\(\varphi \left(r\right)=\sqrt{{r}^{2}+{\sigma }^{2}}\)

Thin Plate Spline

\(\varphi \left(r\right)={r}^{2}/{\mathrm{ln}}r\)

Inverse Multiquadric

\(\varphi \left(r\right)=1/\sqrt{{r}^{2}+{\sigma }^{2}}\)