Extended Radial Basis Functions for Metamodeling: A Comparative Study

The process of constructing computationally benign approximations of expensive computer simulation codes, or metamodeling, is a critical component of several large-scale Multidisciplinary Design Optimization approaches. Such applications typically involve complex models, such as finite elements, computational fluid dynamics, or chemical processes. The decision regarding the most appropriate metamodeling approach usually depends on the type of application. However, several newly-proposed kernel-based metamodeling approaches can provide consistently accurate performance for a wide variety of applications. The authors recently proposed one such novel and effective metamodeling approach — the Extended Radial Basis Function approach — and reported encouraging results. To further understand the advantages and limitations of this new approach, we compare its performance to that of the typical radial basis function approach, and another closely related method — kriging. Several test functions with varying problem dimensions and degrees of nonlinearity are used to compare the accuracies of the metamodels using these metamodeling approaches. We consider several performance criteria, such as metamodel accuracy. effect of sampling technique, effect of problem dimension, and computational complexity. The results suggest that the E-RBF approach is a potentially powerful metamodeling approach for MDO-based applications.