  Total energies of crystal structures can be calculated to high precision
using quantum-based density functional theory (DFT) methods, but the
calculations can be time consuming and scale badly with system size. Cluster
expansions of total energy as a linear superposition of pair, triplet and
higher interactions can efficiently approximate the total energies but are best
suited to simple lattice structures. To model the total energy of boron
carbide, with a complex crystal structure, we explore the utility of machine
learning methods ($L_1$-penalized regression, neural network, Gaussian process
and support vector regression) that capture certain non-linear effects
associated with many-body interactions despite requiring only pair frequencies
as input. Our interaction models are combined with Monte Carlo simulations to
evaluate the thermodynamics of chemical ordering.
