  We present an accurate interatomic potential for graphene, constructed using
the Gaussian Approximation Potential (GAP) machine learning methodology. This
GAP model obtains a faithful representation of a density functional theory
(DFT) potential energy surface, facilitating highly accurate (approaching the
accuracy of ab initio methods) molecular dynamics simulations. This is achieved
at a computational cost which is orders of magnitude lower than that of
comparable calculations which directly invoke electronic structure methods. We
evaluate the accuracy of our machine learning model alongside that of a number
of popular empirical and bond-order potentials, using both experimental and ab
initio data as references. We find that whilst significant discrepancies exist
between the empirical interatomic potentials and the reference data - and
amongst the empirical potentials themselves - the machine learning model
introduced here provides exemplary performance in all of the tested areas. The
calculated properties include: graphene phonon dispersion curves at 0 K (which
we predict with sub-meV accuracy), phonon spectra at finite temperature,
in-plane thermal expansion up to 2500 K as compared to NPT ab initio molecular
dynamics simulations and a comparison of the thermally induced dispersion of
graphene Raman bands to experimental observations. We have made our potential
freely available online at [http://www.libatoms.org].
