We here present a model for real time forecasting of the geomagnetic index Dst. The model consists of a recurrent neural network that has been optimized to be as small as possible without degrading the accuracy. It is driven solely by hourly averages of the solar wind magnetic field component Bz, particle density n, and velocity V, which means that the model does not rely on observed Dst. In an evaluation based on more than 40,000 hours of solar wind and Dst data, it is shown that this model has smaller errors than other models currently in operational use. A complete description of the model is given in an appendix.