A probabilistic method for assisting knowledge extraction from artificial neural networks used for hydrological prediction

Knowledge extraction from artificial neural network weights is a developing and increasingly active field. In the attempt to overcome the ‘black-box’ reputation, numerous methods have been applied to interpret information about the modelled input-to-output relationship that is embedded within the network weights. However, these methods generally do not take into account the uncertainty associated with finding an optimum weight vector, and thus do not consider the uncertainty in the modelled relationship. In order to take this into account, a generic framework for extracting probabilistic information from the weights of an ANN is presented in this paper together with the specific methods used to carry out each stage of the process. The framework is applied to two case studies where the results show that the consideration of uncertainty is extremely important if meaningful information is to be gained from the model, both in terms of an ANN's ability to capture physical input-to-output relations and improving the understanding of the underlying system.