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