Investigation of an adaptive sampling method for data interpolation using radial basis functions

An adaptive sampling method is presented for optimizing the location of data points in parameter space for multidimensional data interpolation. The method requires a small number of points to begin, and achieves a compromise between space-filling updates and local refinement in areas where the data are nonlinear, as measured by the Laplacian. A smooth separation function quantifies the sample spacing, and this is blended with the Laplacian to form a criterion on which to assess potential new sample positions. Validation results are presented using two-dimensional analytic test cases, which demonstrate that the method can recover known optimal designs and gives improvement over data-independent approaches. In addition, a detailed analysis of the various model parameters is presented. Initial findings are very promising, and it is hoped that further work using the method to generate an aerodynamic database using CFD simulations will lead to a reduction in the number of points required for a given modelling accuracy.

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