  Machine learning has shown significant breakthroughs in quantum science,
where in particular deep neural networks exhibited remarkable power in modeling
quantum many-body systems. Here, we explore how the capacity of data-driven
deep neural networks in learning the dynamics of physical observables is
correlated with the scrambling of quantum information. We train a neural
network to find a mapping from the parameters of a model to the evolution of
observables in random quantum circuits for various regimes of quantum
scrambling and test its \textit{generalization} and \textit{extrapolation}
capabilities in applying it to unseen circuits. Our results show that a
particular type of recurrent neural network is extremely powerful in
generalizing its predictions within the system size and time window that it has
been trained on for both, localized and scrambled regimes. These include
regimes where classical learning approaches are known to fail in sampling from
a representation of the full wave function. Moreover, the considered neural
network succeeds in \textit{extrapolating} its predictions beyond the time
window and system size that it has been trained on for models that show
localization, but not in scrambled regimes.
