How Neural Networks Work : The Mathematics of Networks Used to Solve Standard Engineering Problems

Artificial neural networks can be used to learn transfer functions for engineering processes where the production of an analytic mathematical description has proved difficult. Artificial neural networks can provide accurate descriptive models of the system characteristics enabling improved control and optimisation. A major criticism of this technique has been that the only way to establish an appropriate architecture of the network is by trial and error. The application of approximation theory to networks has provided some general theoretical views of network architecture, but these also do not provide any insight into how to practically implement specific networks. In this paper we consider the nodal equations of the networks in terms of their Taylor series expansion, and in doing so produce some results concerning the pragmatics of network architecture. We also introduce an alternative nodal output function, which leads to a method of producing an equivalent transfer function from a trained network.