  Machine learning techniques not only offer efficient tools for modelling
dynamical systems from data, but can also be employed as frontline
investigative instruments for the underlying physics. Nontrivial information
about the original dynamics, which would otherwise require sophisticated ad-hoc
techniques, can be obtained by a careful usage of such methods. To illustrate
this point, we consider as a case study the macroscopic motion emerging from a
system of globally coupled maps. We build a coarse-grained Markov process for
the macroscopic dynamics both with a machine learning approach and with a
direct numerical computation of the transition probability of the
coarse-grained process, and we compare the outcomes of the two analyses. Our
purpose is twofold: on the one hand, we want to test the ability of the
stochastic machine learning approach to describe nontrivial evolution laws, as
the one considered in our study; on the other hand, we aim at gaining some
insight into the physics of the macroscopic dynamics by modulating the
information available to the network, we are able to infer important
information about the effective dimension of the attractor, the persistence of
memory effects and the multi-scale structure of the dynamics.
