Draft: an Approach towards Generating Surrogate Models by Using Rbfn with a Priori Bias

In this paper, an approach to generate surrogate models constructed by radial basis function networks (RBFN) with a priori bias is presented. RBFN as a weighted combination of radial basis functions only, might become singular and no interpolation is found. The standard approach to avoid this is to add a polynomial bias, where the bias is defined by imposing orthogonality conditions between the weights of the radial basis functions and the polynomial basis functions. Here, in the proposed a priori approach, the regression coefficients of the polynomial bias are simply calculated by using the normal equation without any need of the extra orthogonality prerequisite. In addition to the simplicity of this approach, the method has also proven to predict the actual functions more accurately compared to the RBFN with a posteriori bias. Several test functions, including Rosenbrock, Branin-Hoo, Goldstein-Price functions and two mathematical functions (one large scale), are used to evaluate the performance of the proposed method by conducting a comparison study and error analysis between the RBFN with a priori and a posteriori known biases. Furthermore, the aforementioned approaches are applied to an engineering design problem, that is modeling of the material properties of a three phase spherical graphite iron (SGI) . The corresponding surrogate models are presented and compared.