Near-Earth space processes are highly nonlinear. Since the 1990s, a small group at the Middle East Technical University in Ankara has been working on a data-driven generic model of such processes, that is, forecasting and nowcasting of a near-Earth space parameter of interest. The model developed is called the Middle East Technical University Neural Network (METU-NN) model. The METU-NN is a data-driven neural network model of one hidden layer and several neurons. In order to understand more about the complex response of the magnetosphere and ionosphere to extreme solar events, we chose this time the series of space weather events in November 2003. Total electron content (TEC) values of the ionosphere are forecast during these space weather events. In order to facilitate an easier interpretation of the forecast TEC values, maps of TEC are produced by using the Bezier surface-fitting technique.