Abstract
Recent artificial neural network research has focused on simple models, but such models have not proved very successful in describing complex systems. Neural network group theory is a step towards bridging this gap between simple models and complex systems. We first develop artificial neural network group theory, then proceed to show how neural network groups are able to approximate any kind of piecewise continuous function, and to any degree of accuracy. These principles are then illustrated by way of an ANN expert system for rainfall estimation. It is shown that using this approach, rainfall estimates can be computed around 10 times faster than conventional techniques, and with average errors for the overall precipitation event falling below 10%. Based on our work to date, we conclude that neural network group theory holds considerable potential for complex problem solving in various domains.
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