  Predicting phase stabilities of crystal polymorphs is central to
computational materials science and chemistry. Such predictions are challenging
because they first require searching for potential energy minima and then
performing arduous free-energy calculations to account for entropic effects at
finite temperatures. Here, we develop a framework that facilitates such
predictions by exploiting all the information obtained from random searches of
crystal structures. This framework combines automated clustering,
classification and visualisation of crystal structures with machine-learning
estimation of their enthalpy and entropy. We demonstrate the framework on the
technologically important system of TiO2, which has many polymorphs, without
relying on prior knowledge of known phases. We find a number of new phases and
predict the phase diagram and metastabilities of crystal polymorphs at 1600 K,
benchmarking the results against full free-energy calculations.
