Investigating phase transitions with machine learning methods

Phase transitions occur in a variety of settings and situations in particle physics, condensed matter and statistical mechanics. The traditional approach to phase transitions, based on elegant principles such as scaling and universality, assumes some basic a priori knowledge of the physical system, in particular of the Hamiltonian and its underlying symmetries. While this information is usually given for granted, a data-driven approach has wider applicability. In this talk, I will present some applications of machine learning starting from Monte-Carlo generated data for phase transitions in simple (but far from trivial!) statistical and quantum field theoretical systems. More in details, I will discuss (a) identification of symmetries; (b) constructions of order parameters; and (c) precise determination of critical temperature and critical exponents. I will conclude showing how machine learning can be used to invert a renormalisation group flow.