  Finding proper collective variables for complex systems and processes is one
of the most challenging tasks in simulations, which limits the interpretation
of experimental and simulated data and the application of enhanced sampling
techniques. Here, we propose a machine learning approach able to distill few,
physically relevant variables by associating instantaneous configurations of
the system to their corresponding inherent structures as defined in liquids
theory. We apply this approach to the challenging case of structural
transitions in nanoclusters, managing to characterize and explore the
structural complexity of an experimentally relevant system constituted by 147
gold atoms. Our inherent-structure variables are shown to be effective at
computing complex free-energy landscapes, transition rates, and at describing
non-equilibrium melting and freezing processes. The effectiveness of this
machine learning strategy guided by the generally-applicable concept of
inherent structures shows promise to devise collective variables for a vast
range of systems, including liquids, glasses, and proteins.
