Ground-based aircraft trajectory prediction is a major concern in air traffic control and management. A safe and efficient prediction is a prerequisite to the implementation of new automated tools. In current operations, trajectory prediction is computed using a physical model. It models the forces acting on the aircraft to predict the successive points of the future trajectory. Using such a model requires knowledge of the aircraft state (mass) and aircraft intent (thrust law, speed intent). Most of this information is not available to ground-based systems. Focusing on the climb phase, we train neural networks to predict some of the unknown point-mass model parameters. These unknown parameters are the mass and the speed intent. For each unknown parameter, our model predicts a Gaussian distribution. This predicted distribution is a predictive distribution: it is the distribution of possible unknown parameter values conditional to the observed past trajectory of the considered aircraft. Using this distribution, one can extract a predicted value and the uncertainty related to this specific prediction. Using a physical model like BADA, this distribution could be used to derive a probability distribution of possible future trajectory ([1]). This study relies on ADS-B data coming from The OpenSky Network. It contains the climbing segments of the year 2017 detected by this sensor network. The 11 most frequent aircraft types are studied. The obtained data set contains millions of climbing segments from all over the world. Using this data, we show that despite having an RMSE slightly larger than previously tested methods, the predicted uncertainty allows us to reduce the size of prediction intervals while keeping the same coverage probability. Furthermore, we show that the trajectories with a similar predicted uncertainty have an observed RMSE close to the predicted one. The data set and the machine learning code are publicly available.