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Machine learning techniques not only offer efficient tools for modellingdynamical systems from data, but can also be employed as frontlineinvestigative instruments for the underlying physics. Nontrivial informationabout the original dynamics, which would otherwise require sophisticated ad-hoctechniques, can be obtained by a careful usage of such methods. To illustratethis point, we consider as a case study the macroscopic motion emerging from asystem of globally coupled maps. We build a coarse-grained Markov process forthe macroscopic dynamics both with a machine learning approach and with adirect numerical computation of the transition probability of thecoarse-grained process, and we compare the outcomes of the two analyses. Ourpurpose is twofold: on the one hand, we want to test the ability of thestochastic machine learning approach to describe nontrivial evolution laws, asthe one considered in our study; on the other hand, we aim at gaining someinsight into the physics of the macroscopic dynamics by modulating theinformation available to the network, we are able to infer importantinformation about the effective dimension of the attractor, the persistence ofmemory effects and the multi-scale structure of the dynamics.

Using machine-learning modelling to understand macroscopic dynamics in a system of coupled maps