Efficient voronoi metamodelling for large scale approximation

This paper presents a novel metamodel formulation for efficient function emulation based on Radial Basis Function (RBF) interpolation. Lattice sampling plans and the geometry of the Voronoi tessellation are exploited to localise the RBF interpolation with the aim of increasing efficiency for large scale modelling with minimum loss of global accuracy. The performance of the proposed technique is examined using standard test problems and compared to established global and compact RBF modelling techniques. The fitting and prediction times for the new method are shown to be linearly proportional to the number of sample points allowing large data sets to be handled without prohibitive growth in computational cost. Accuracy is shown to be comparable to that of the global RBF for problems of medium to low dimensionality.