  We introduce a Gaussian approximation potential (GAP) for atomistic
simulations of liquid and amorphous elemental carbon. Based on a
machine-learning representation of the density-functional theory (DFT)
potential-energy surface, such interatomic potentials enable materials
simulations with close-to DFT accuracy but at much lower computational cost. We
first determine the maximum accuracy that any finite-range potential can
achieve in carbon structures; then, using a novel hierarchical set of two-,
three-, and many-body structural descriptors, we construct a GAP model that can
indeed reach the target accuracy. The potential yields accurate energetic and
structural properties over a wide range of densities; it also correctly
captures the structure of the liquid phases, at variance with state-of-the-art
empirical potentials. Exemplary applications of the GAP model to surfaces of
"diamond-like" tetrahedral amorphous carbon (ta-C) are presented, including an
estimate of the amorphous material's surface energy, and simulations of
high-temperature surface reconstructions ("graphitization"). The new
interatomic potential appears to be promising for realistic and accurate
simulations of nanoscale amorphous carbon structures.
