Data-driven prediction in quantum mechanics consists in providing an approximative description of the motion of any particles at any given time, from data that have been previously collected for a certain number of particles under the influence of the same Hamiltonian. The difficulty of this problem comes from the ignorance of the exact Hamiltonian ruling the dynamic. In order to address this problem, we formulate an inverse problem consisting in determining the Hamiltonian of a quantum system from the knowledge of the state at some fixed finite time for each initial state. In this talk, I will report a uniqueness theorem for this inverse problem, which is a joint collaboration with Alberto Ruiz.