X-ray reflectivity (XRR) is a powerful and popular scattering technique that can give valuable insight into the growth behavior of thin films. In this study, we show how a simple artificial neural network model can be used to predict the thickness, roughness and density of thin films of different organic semiconductors (diindenoperylene, copper(II) phthalocyanine and $\alpha$-sexithiophene) on silica from their XRR data with millisecond computation time and with minimal user input or a priori knowledge. For a large experimental dataset of 372 XRR curves, we show that a simple fully connected model can already provide good predictions with a mean absolute percentage error of 8-18 % when compared to the results obtained by a genetic least mean squares fit using the classical Parratt formalism. Furthermore, current drawbacks and prospects for improvement are discussed.