We present a new force field and development scheme for atomistic simulations of materials under extreme conditions. These models, which explicitly include two- and three-body interactions, are generated by fitting linear combinations of Chebyshev polynomials through force matching to trajectories from Kohn–Sham density functional theory (DFT). We apply our method to liquid carbon near the diamond/graphite/liquid triple point and at higher densities and temperatures, where metallization and many-body effects may be substantial. We show that explicit inclusion of three-body interaction terms allows our model to yield improved descriptions of both dynamic and structural properties over previous empirical potential efforts, while exhibiting transferability to nearby state points. The simplicity of our functional form and subsequent efficiency of parameter determination allow for extension of DFT to experimental time and length scales while retaining most of its accuracy.