Artificial neural networks (ANNs) have been increasingly used as a model for streamflow forecasting, time series prediction, and other applications. The high interest in ANNs comes from their ability to approximate complex nonlinear functions. However, the "black-box" nature of ANN models makes it difficult for researchers to design network structure or to physically interpret the variables involved. Recent investigations in ANN research have found connections linking ANNs and statistics-based regression modeling. By comparing the two modeling structures, new insight can be gained on the functionality of ANNs.

This study investigates two primary relationships between ANN and statistical models: the potential equivalence between feed-forward neural networks (FNN) and multiple polynomial regression (MPR) models and the potential equivalence between recurrent neural networks (RNN) and auto-regressive moving average (ARMA) models. Equivalence is determined through both formal and empirical methods. The real-world phenomenon of streamflow forecasting is used to verify the equivalences found.

Results indicate that both FNNs and RNNs can be designed to replicate many regression equations. It was also found that the optimal number of hidden nodes in an ANN is directly dependant on the order of the underlying physical equation being modeled. These simple relationships can be expanded to more complex models in future research.