  Finding the dynamical law of observable quantities lies at the core of
physics. Within the particular field of statistical mechanics, the generalized
Langevin equation (GLE) comprises a general model for the evolution of
observables covering a great deal of physical systems with many degrees of
freedom and an inherently stochastic nature. Although formally exact, the GLE
brings its own great challenges. It depends on the complete history of the
observables under scrutiny, as well as the microscopic degrees of freedom, all
of which are often inaccessible. We show that these drawbacks can be overcome
by adopting elements of machine learning from empirical data, in particular
coupling a multilayer perceptron (MLP) with the formal structure of the GLE and
calibrating the MLP with the data. This yields a powerful computational tool
capable of describing noisy complex systems beyond the realms of statistical
mechanics. It is exemplified with a number of representative examples from
different fields: from a single colloidal particle and particle chains in a
thermal bath to climatology and finance, showing in all cases excellent
agreement with the actual observable dynamics. The new framework offers an
alternative perspective for the study of non-equilibrium processes opening also
a new route for stochastic modelling.
