Predictions of the daily solar wind velocity (V) at 1 AU from the flux tube expansion factor fs are examined with radial basis function neural networks. The flux tube expansion factor is calculated from the potential field model, using Wilcox Solar Observatory magnetograms, with the source surface placed at 2.5 solar radii. The time series extend over 20 years from 1976 to 1995 and consist of approximately 3000 daily values of fs and V. The correlation between monthly averages of 1/fs and V is 0.57, independent of the assumed Sun-Earth solar wind travel time &tgr;. However, for daily averages the correlation drops to 0.38 with &tgr;=5 days. Even adjusting &tgr; to match the observed velocity does not improve on the overall correlation. A time series of fs(t) extending over t-4 to t is used as input to the neural network. The network is trained to predict the solar wind velocity V(t+2) 2 days ahead. The overall correlation on a test set, not included in the training, is 0.53, and the root-mean-square error is 85 km/s. Although the increase is significant, the correlation is still low. However, by studying a number of test cases it is seen that high-speed streams originating from coronal holes are well predicted, while transient structures related to coronal mass ejections are not predicted. To go further, a more detailed description of the solar magnetic fields must be included. The potential field model does not describe the currents in the corona, and changes of the photospheric magnetic field from day to day are smoothed out. By examining the relative error of the calculated photospheric magnetic field and the observed field, it is shown that the correlation between 1/fs(t) and V(t+5) increases to 0.47 for errors smaller than 20% and drops to 0.3 for errors larger than 34%. ¿ 1999 American Geophysical Union