Coronal Mass Ejections (CMEs) are large eruptions of plasma ejected into the heliosphere. They are significant for space weather forecast, as regards their time of arrival at Earth. In this respect, the kinematics of most CMEs can be described by a long-standing deterministic model, named Drag-Based Model (DBM) (see, e.g., Cargill 2004, Vršnak et al. 2010). However, the DBM poses two main limitations: 1) it fails with CMEs accelerated/decelerated more than the background solar wind; 2) it requires that the CME drag coefficient is measured with high accuracy, which is generally not the case. As opposed to purely data-driven Machine Learning or deterministic approaches, in the present study we combine the two of them. First, we propose a simple extension of the DBM capable of targeting also CMEs propelled beyond the solar wind speed. Second, following Guastavino et al. 2023, we exploit the analytical solutions $r(t)$ and $r(v)$ of the model, where $t,r,v$ stand respectively for time, distance and speed, to train neural networks fed with remote sensing, in situ and synthetic data aimed at determining the uncertain dynamical parameters of the CME given its initial conditions. Consequently, we provide an estimate of the speed and time of arrival at Earth.