Simple Neural Networks as Wavefront Slope Predictors: Training and Performance Issues

Artificial neural networks have gained significant popularity over the past several years in a wide variety of engineering applications. This popularity is due in part to the ability of a neural network that is trained using a supervised training rule such as error backpropagation to acquire a nonparametric representation of the mapping between a set of inputs and outputs without any specific knowledge of the application domain. Given a sufficient number of nonlinear terms, represented by a number of hidden-layer neurons, a multilayer neural network can model any mathematical function that is continuous and differentiable (Hecht-Nielsen, 1990). Difficulties can arise however when a network is trained with a limited amount of noisy “real” data and is then expected to operate as part of a system for a specific application. The network must acquire an internal representation, as stored in its weights, during the training phase that subsequently generalizes well to unseen data. In the case of a prediction application, generalization capability becomes the paramount design criteria. The generalization performance of a trained network is a strong function of several factors, including: the architecture and complexity of the network, the type of supervised training rule employed, and the manner in which data is preprocessed and presented to the network.