Over-parameterisation, a major obstacle to the use of artificial neural networks in hydrology?

Abstract

Recently Feed-Forward Artificial Neural Networks (FNN) have been gaining popularity for stream flow forecasting. However, despite the promising results presented in recent papers, their use is questionable. In theory, their “universal approximator‿ property guarantees that, if a sufficient number of neurons is selected, good performance of the models for interpolation purposes can be achieved. But the choice of a more complex model does not ensure a better prediction. Models with many parameters have a high capacity to fit the noise and the particularities of the calibration dataset, at the cost of diminishing their generalisation capacity. In support of the principle of model parsimony, a model selection method based on the validation performance of the models, 'traditionally' used in the context of conceptual rainfall-runoff modelling, was adapted to the choice of a FFN structure. This method was applied to two different case studies: river flow prediction based on knowledge of upstream flows, and rainfall-runoff modelling. The predictive powers of the neural networks selected are compared to the results obtained with a linear model and a conceptual model (GR4j). In both case studies, the method leads to the selection of neural network structures with a limited number of neurons in the hidden layer (two or three). Moreover, the validation results of the selected FNN and of the linear model are very close. The conceptual model, specifically dedicated to rainfall-runoff modelling, appears to outperform the other two approaches. These conclusions, drawn on specific case studies using a particular evaluation method, add to the debate on the usefulness of Artificial Neural Networks in hydrology. Keywords: forecasting; stream-flow; rainfall-runoff; Artificial Neural Networks