Improved accuracy considerations in Radial Basis Function surrogate models for variable resolution, scale, dimension and discontinuity

Abstract

Surrogate- or metamodels approximate and so reduce the computational cost associated with evaluating computer experiments of interest over a set of design variables. Radial Basis Functions (RBFs) are a popular metamodel choice due to its ease of implementation and availability in popular scientific programming languages. The correct use of RBF metamodels first require a model appropriate choice of basis function. The inclusion of a higher level model definition, using a polynomial for example, is another important consideration. By using cross-validation, dimensional scaling and error indicators calculated and inherited from Bayesian statistics or Machine Learning algorithms, the accuracy of the surrogate approximation can further be improved. Multiple surrogates may also be needed if discontinuities exist within the design space of the underlying computer experiment. In this conference contribution, many of these non-standard considerations are addressed and illustrated. The work focuses on the knowledge transfer and correct use of RBF surrogate models. The model implementation and considerations are first illustrated on benchmark test functions. This is followed by a CFD test-problem on the particular use of RBFs to construct a flight envelope of an object, illustrated using the interaction of two diamond airfoils. The test-problem shows the practical design of an RBF surrogate considering non-linearities in the drag, lift and moment coefficients as a result of interaction between various shock waves in the transonic and supersonic regime.