Functional activity in the brain is associated with the generation of currents and resultant voltages which may be observed on the scalp as the electroencephelogram. The current sources may be modeled as dipoles. The properties of the current dipole sources may be studied by solving either the forward or inverse problems. The forward problem utilizes a volume conductor model for the head, in which the potentials on the conductor surface are computed based on an assumed current dipole at an arbitrary location, orientation, and strength. In the inverse problem, on the other hand, a current dipole, or a group of dipoles, is identified based on the observed EEG. Both the forward and inverse problems are typically solved by numerical procedures, such as a boundary element method and an optimization algorithm. These approaches are highly time-consuming and unsuitable for the rapid evaluation of brain function. In this paper we present a different approach to these problems based on machine learning. We solve both problems using artificial neural networks which are trained off-line using back-propagation techniques to learn the complex source-potential relationships of head volume conduction. Once trained, these networks are able to generalize their knowledge to localize functional activity within the brain in a computationally efficient manner.