  We investigate the potential of supervised machine learning to propagate a
quantum system in time. While Markovian dynamics can be learned easily, given a
sufficient amount of data, non-Markovian systems are non-trivial and their
description requires the memory knowledge of past states. Here we analyse the
feature of such memory by taking a simple 1D Heisenberg model as many-body
Hamiltonian, and construct a non-Markovian description by representing the
system over the single-particle reduced density matrix. The number of past
states required for this representation to reproduce the time-dependent
dynamics is found to grow exponentially with the number of spins and with the
density of the system spectrum. Most importantly, we demonstrate that neural
networks can work as time propagators at any time in the future and that they
can be concatenated in time forming an autoregression. Such neural-network
autoregression can be used to generate long-time and arbitrary dense time
trajectories. Finally, we investigate the time resolution needed to represent
the system memory. We find two regimes: for fine memory samplings the memory
needed remains constant, while longer memories are required for coarse
samplings, although the total number of time steps remains constant. The
boundary between these two regimes is set by the period corresponding to the
highest frequency in the system spectrum, demonstrating that neural network can
overcome the limitation set by the Shannon-Nyquist sampling theorem.
