Data Assimilation remains the operational choice when it comes to forecast and estimate Earth's dynamical systems. The analogy with Machine Learning has already been shown and is still being investigated to address the problem of improving physics-based models. Even though both techniques learn from data, machine learning focuses on inferring models while data assimilation concentrates on hidden system state estimation with the help of a dynamical model. In this work, we exploit the complementarity of these methods in a twin experiment where the system is partially observed and the known dynamics are incomplete. Finally, we succeed in partially retrieving the dynamics of a fully-unobserved variable by training a hybrid model through variational data assimilation.