Optimal Weighted Pointwise Ensemble of Radial Basis Functions with Different Basis Functions

The radial basis functions (RBF) interpolation model has been extensively used in various engineering fields. All these applications call for accurate RBF models. The RBF predictions are affected by the choice of basis functions, whereas the proper basis function is problem dependent. To avoid the choice of basis functions and improve the predictions, this paper presents an optimal weighted pointwise ensemble (OWPE) to combine the locally accurate predictions of RBF models built with different basis functions together. The key to the success of OWPE is to construct proper pointwise weight functions for the component RBF models. At the observed points, the weights of one or zero were used to sufficiently highlight the locally accurate predictions of component RBF models. At the unobserved points, the optimal pointwise weight functions were constructed by using an optimized coefficient that can adapt to the characteristics of component RBF models. Numerical experiments on 14 analytical functions and an axial compressor blade design example show that OWPE provides more accurate and robust predictions. Additionally, OWPE performs better when having more observed points and component RBF models. It is notable that OWPE can also be used with other types of interpolation metamodels.