  Structural phase transitions as a function of temperature dictate the
structure--functionality relationships in many technologically important
materials. Harmonic Hamiltonians have proven successful in predicting the
vibrational properties of many materials. However, they are inadequate for
modeling structural phase transitions in crystals with potential energy
surfaces that are either strongly anharmonic or no\ n-convex with respect to
collective atomic displacements or homogeneous strains. In this paper we
develop a framework to express highly anharmonic first-principles potential
energy surfaces as polynomials of collective cluster deformati\ ons. We further
adapt the approach to a nonlinear extension of the cluster expansion formalism
through the use of an artificial neural net model. The machine learning models
are trained on a large database of first-principles calculations and are shown
to reproduce the potential energy surface with l\ ow error.
