A comparison of the von Mises and Gaussian basis functions for approximating spherical acoustic scatter

This paper compares the approximation accuracy of two basis functions that share a common radial basis function (RBF) neural network architecture used for approximating a known function on the unit sphere. The basis function types considered are that of a new spherical basis function, the von Mises function, and the now well-known Gaussian basis function. Gradient descent learning rules were applied to optimize (learn) the solution for both approximating basis functions. A benchmark approximation problem was used to compare the performance of the two types of basis functions, in this case the mathematical expression for the scattering of an acoustic wave striking a rigid sphere.