A multi-level approach seems promising rather than directly learning the most expensive model from the structural descriptors. This is because the force field energies are already in-hand for every structure as a result of the global structure search, and are based on FIT+DMA, a physically motivated force field that provides a good baseline. This is clear from the correlation to PBE lattice energies (Fig. ). In particular, FIT+DMA provides accurate electrostatic energies, whose long range might be impossible to model accurately based on descriptors of local atomic environments. Furthermore, since most physics of the problem is captured at the PBE level, the PBE/PBE0 linear correlation (Fig. ) is very high (R 2 ≈ 0.98) and so much of the relationship between the expensive PBE0 energies and the structural descriptor can be learned from PBE calculations, at a much reduced computational cost. From these features, we anticipate model (1) being successful with parameter ρ capturing the strong linear relationship between PBE and PBE0. Inadequacies in a simple linear correlation will be described with the GPR prior on the difference δ , and learning δ allows efficient prediction of PBE0 energies using less expensive evaluations of PBE.