Radial Basis Function
Uses linear combinations of basis functions, such as linear, cubic, thinplate spline, Gaussian, multiquadric, and inversemultiquadric. These basis functions are observed to be accurate for highly nonlinear output responses but not for linear output responses.
where $n$ is the number of sampling points, $x$ is a vector of input variables, ${x}_{i}$ is the i^{th} sampling point, $\Vert x{x}_{i}\Vert $ is the Euclidean norm, $\varphi $ is a basis function, and ${\lambda}_{i}$ is the coefficient for the i^{th} basis function. ${p}_{j}(x)$ is a loworder (constant or linear) polynomial function; $k$ is the total number of terms in the polynomial, and $cj(j=1,\mathrm{2...}k)$ are the unknown coefficients.
Usability Characteristics
 Attempts to go through the exact sampling points, and in general, the residuals are small, if not zero. As a result, diagnostic measures using only the complete input matrix do not produce meaningful values. Crossvalidation results provide some diagnostics using a special scheme using only the input points. To get detailed diagnostics on the quality of a Radial Basis Function Fit, it is suggested that you use a testing matrix.
 Suitable for modeling highly nonlinear output response data that does not contain numerical noise.
 Applicability of HyperKriging and Radial Basis Function methods are similar in terms of physics (they both are suggested for
highly nonlinear output responses with no noise). It is suggested that you
use HyperKriging for large studies that contain a large
number of sampling points, whereas, Radial Basis Function is
suggested for studies with a large number of variables.Note: As a result, Radial Basis Function Fit are evaluated faster than HyperKriging Fits when used in approaches.
Settings
Parameter  Default  Range  Description 

Augmented Function  Constant 

Type of augmented function. 
Maximum Points  2000  >=100  Maximum number of points for building Radial Basis Function; if number of building points is larger than maxnpt, then the point reduction algorithm is activated and a warning message is shown; the purpose of introducing maxnpt is to reduce computational effort for large scale problems. 
RBF Type  CS21  Multiquadric CS21 (formally knows as Wu's Compactly Supported (2,1)) Gaussian 
Type of Radial Basis Function. 
Relaxation Parameters  1.0  >=0.0  Relaxation parameter d used in Radial Basis Function; if Radial Basis Function is CS21 or Gaussian, and d is set to 0.0 by users, then Radial Basis Function will automatically set d = 1.0e6. 