  We introduce a new method, called CNNAS (convolutional neural networks for
atomistic systems), for calculating the total energy of atomic systems which
rivals the computational cost of empirical potentials while maintaining the
accuracy of \emph{ab initio} calculations. This method uses deep convolutional
neural networks (CNNs), where the input to these networks are simple
representations of the atomic structure. We use this approach to predict
energies obtained using density functional theory (DFT) for 2D hexagonal
lattices of various types. Using a dataset consisting of graphene, hexagonal
boron nitride (hBN), and graphene-hBN heterostructures, with and without
defects, we trained a deep CNN that is capable of predicting DFT energies to an
extremely high accuracy, with a mean absolute error (MAE) of 0.198 meV / atom
(maximum absolute error of 16.1 meV / atom). To explore our new methodology, we
investigate the ability of a deep neural network (DNN) in predicting a
Lennard-Jones energy and separation distance for a dataset of dimer molecules
in both two and three dimensions. In addition, we systematically investigate
the flexibility of the deep learning models by performing interpolation and
extrapolation tests.
