  High throughput screening of materials for technologically relevant areas,
like identification of better catalysts, electronic materials, ceramics for
high temperature applications and drug discovery, is an emerging topic of
research. To facilitate this, density functional theory based (DFT)
calculations are routinely used to calculate the electronic structure of a wide
variety of materials. However, DFT calculations are expensive and the computing
cost scales as the cube of the number of electrons present in the system. Thus,
it is desirable to generate surrogate models that can mitigate these issues. To
this end, we present a two step procedure to predict total energies of large
three-dimensional systems (with periodic boundary conditions) with chemical
accuracy (1kcal/mol) per atom using a small data set, meaning that such models
can be trained on-the-fly. Our procedure is based on the idea of the
Hohenberg-Kohn map proposed by Brockherde et al. (Nat. Commun, 8, 872 (2017))
and involves two training models: one, to predict the ground state charge
density, $\rho(r)$, directly from the atomic structure, and another to predict
the total energy from $\rho(r)$. To predict $\rho(r)$, we use many-body
correlation descriptors to accurately describe the neighborhood of a grid point
and to predict the total energy we use amplitudes of these many-body
correlation descriptors. Utilizing the amplitudes of the many-body descriptors
allows for uniquely identifying a structure while accounting for constraints,
such as translational invariance; additionally, such a formulation is
independent of the charge density grid.
