A Small Note on Artificial Neural Networks and GIS
Artificial Neural Networks or ANNs as we popularly known are models that are designed to imitate the human brain through the use of Mathematical Models.
ANNs have been applied to problems like classification, time series analysis, wave/wind speed predictions, etc.
Most of the natural phenomenon are inherently random in nature and cannot be effectively represented or formulated as a series of Mathematical Equations.
ANNs have been proved to be successful in modelling such phenomenon as we can see in several publications citing to Wave Speed Prediction or Wind Speed Prediction .
( Iam citing Civil Engineering applications for the obvious reasons).
ANNs can be tightly coupled with GIS to create highly intelligent decision support systems(DSS).
One such example can be a GIS based Navigation System:-
On any given day vehicular traffic will vary through a city with respect to time of day, road network capacity and weather amongst other factors. A GIS can map the road network easily enough, but imagine an accident or some other event causing this flow of traffic to change. Traffic congestion would change with respect to other routes, those nearer the event becoming more congested. ANN input might include the location of the accident causing resultant congestion on arterial roadways, current weather conditions which influence speed and time of day, which relates to load. Using ANN all variables with respect to the accident could be processed resulting in a determination of optimum re-routing until the traffic flow is stabilized. In such a case, GIS mapping is used and spatial data acts as one of the input variables into the ANN. Taken one step further, a map server could update with latest conditions and transfer those to vehicles and or PDA – allowing individual drivers to follow the best selected re-routing. This would also be quite useful for emergency vehicle access purposes. 
Intellligent Planning Tool
Other example would be an intelligent GIS based tool for Fire Station Locations planning for future. This would involve prediction of location of fire incidents based on the location of past data. As I believe that ANN can extract a pattern from the past fire location data to predict the future locations. The Data which is obtained based on ANN predictions can be fed to a GIS based Simulation Software  which could predict the optimum location of fire stations for future years. I would also like to mention that this is a GIS-T application since it involves travel time optimisation on road networks.
[ I would like to work on this if I get funding !! for it ]
Finally I conclude that we would get the maximum utilization of GIS based Decision Support Systems and Artificial Intelligent techniques like ANN, heristics, etc when they are coupled together to solve real world problems.
 "Wind Speed Analysis using Artificial Neural Networks", Sandeep Kumar Jakkaraju, B Tech Project, Civil Engineering Department, IIT Bombay. (2001) [unpublished]
 "GIS & Artificial Neural Networks: Does Your GIS Think?" , Jeff Thurston - January 2002 GISCafe.com.
 Simulation of Fire Company Response Times, Jean-Claude Thill, Irene Casas, Sandeep Kumar Jakkaraju (SUNY-Buffalo) ,50th Annual North American Meetings of the Regional Science Association International, Philadelphia, Pennsylvania, Nov 20-22, 2003.
[ copyright Sandeep Kumar Jakkaraju , 2006]