As part of the POWADIMA research project, this paper describes the technique used to predict the consequences of different control settings on the performance of the water-distribution network, in the context of real-time, near-optimal control. Since the use of a complex hydraulic simulation model is somewhat impractical for real-time operations as a result of the computational burden it imposes, the approach adopted has been to capture its domain knowledge in a far more efficient form by means of an artificial neural network (ANN). The way this is achieved is to run the hydraulic simulation model off-line, with a large number of different combinations of initial tank-storage levels, demands, pump and valve settings, to predict future tank-storage water levels, hydrostatic pressures and flow rates at critical points throughout the network. These input/output data sets are used to train an ANN, which is then verified using testing sets. Thereafter, the ANN is employed in preference to the hydraulic simulation model within the optimization process. For experimental purposes, this technique was initially applied to a small, hypothetical water-distribution network, using EPANET as the hydraulic simulation package. The application to two real networks is described in subsequent papers of this series.