Product-Units neural networks for catchment runoff forecasting

In this paper Product-Units neural networks (PUNNs), which probably have never been used within the field of hydrology, are introduced and applied for catchment runoff forecasting in cold climate zones. This type of neural networks, a subclass of higher order neural networks uses product nodes with inputs raised to exponential weights in one layer and well-known summation nodes in another layer. The present paper empirically shows that PUNNs with unbounded weights are difficult to train and do not perform well for catchment runoff forecasting. However, a very good predictive performance may be achieved when the weights are bounded within [−1, 1] interval. Several variants of optimization methods, mostly Differential Evolution-based algorithms, and a few approaches enabling good generalization capabilities of neural networks are compared in order to select the appropriate technique for PUNNs training. PUNNs with parameters bounded within [−1, 1] interval are shown to outperform Multi-Layer Perceptron neural networks and HBV conceptual model for runoff forecasting case study at Annapolis River, Nova Scotia, Canada. Gradient-based Levenberg–Marquardt algorithm and Evolutionary Computation-based Differential Evolution with Global and Local Neighborhood method turn out to be the most successful among the tested training algorithms. Surprisingly, in the case of Product-Units neural networks with weights bounded within [−1, 1] interval using noise injection or early stopping do not improve the results obtained when no method to avoid overfitting is used.