The Hohenberg-Kohn theorems posit the ground state electron density as a property of fundamental importance in condensed matter physics, finding widespread application in much of solid state physics in the form of density functional theory (DFT) and, at least in principle, in semi-empirical potentials such as the Embedded Atom Method (EAM). Using machine learning algorithms based on parametric linear models, we propose a systematic approach to developing such potentials for binary alloys based on DFT electron densities, as well as energies and forces. The approach is demonstrated on the technologically important Al-Ni alloy system. We further demonstrate how ground state electron densities, obtained with DFT, can be predicted such that total energies have an accuracy of order meV atom−1 for crystalline structures. The set of crystalline structures includes a range of materials representing different phases and bonding types, from Al structures to single-wall carbon nanotubes.