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Interpolation[funcvaluelist,Method→"RBF",(options)] represents a way to perform interpolation utilizing radial basis functions when funcvaluelist is a list of scattered control points together with the function values in these points. 
DistanceFunction  Automatic  distance function to use in calculation of the distance matrix and the calculation of the distance from the interpolation point to the control points. Note, that the function here is expected to return the square of the distance  
RadialBasisFunction  Automatic  Radial Basis Function required by the RBF interpolation method 
If the same interpolation should be used in many different points, the function can be precompiled without specifying in which point it will be used. Note, in the plot below, that extrapolation is used along the border of the plot. As seen, this method has in this case strong predictive capability also for extrapolation.
