Performance comparizon of unorganized recurrent neural network applied to streamflow forecasting of Sobradinho plant

Abstract

Echo state networks can be safely regarded as promising tools in time series forecasting because they are recurrent networks which have a simple and efficient training process based on a linear regression. The recurrent character of an ESN comes from a dynamic reservoir that corresponds to a hidden layer with feedback loops which remains untrained, whereas its output layer is an adjustable linear combiner. Recently, Boccato et al. proposed a new architecture in which the output layer is built using a data compression method — principal component analysis — and a Volterra filter. Interestingly, this idea does not compromise the simplicity of the training process, once the output remains linear with respect to the free parameters and the PCA stage prevents any risk coming from a potential curse of dimensionality. This work performs a comparative investigation among the performances of different ESNs architectures in the context of the forecasting of monthly seasonal streamflow series associated with Sobradinho hydroelectric plant. Two possible reservoir design approaches are tested with the classical and the Volterra-based output layer structures, and a multilayer perceptron is also included to establish bases for comparison with feedforward solutions. The results obtained from this study show the relevance of echo state networks to the problem of modeling seasonal streamflow series and also contribute to a better understanding of the applicability of these networks to forecasting problems in general.