Using Function Approximation to Determine Neural Network Accuracy

Many, if not most, control processes demonstrate non-linear behavior in some portion of their operating range and the ability of neural networks to model non-linear dynamics makes them very appealing for control. Control of high reliability safety systems, and autonomous control in process or robotic applications, however, require accurate and consistent control and neural networks are only approximators of various functions so their degree of approximation becomes important. In this paper, the factors affecting the ability of a feed-forward back-propagation neural network to accurately approximate a non-linear function are explored. Compared to pattern recognition using a neural network for function approximation provides an easy and accurate method for determining the network's accuracy. In contrast to other techniques, we show that errors arising in function approximation or curve fitting are caused by the neural network itself rather than scatter in the data. A method is proposed that provides improvements in the accuracy achieved during training and resulting ability of the network to generalize after training. Binary input vectors provided a more accurate model than with scalar inputs and retraining using a small number of the outlier x,y pairs improved generalization.