Common Misconceptions about Neural Networks as Approximators

Abstract
A current trend in scientific and engineering computing is to use neural‐network approximations instead of polynomial approximations or other types of approximations involving mathematical functions. A number of misconceptions have arisen concerning neural networks as approximators. This paper eliminates these misconceptions. In so doing, the paper examines the computational efficiency of neural‐network approximations compared to polynomial approximations, examines the effect of using underdetermined neural‐network approximations, examines the effect of design point selection on the quality of neural‐network approximations, and examines the computing time required to train neural networks compared to the time to develop polynomial approximations.