  Cluster expansion approximates an on-lattice potential with polynomial
regression. We show that using a convolutional neural network (CNN) instead
leads to more accurate prediction due to the depth of the network. We construct
our CNN potential directly on cubic lattice sites, representing voxels in a 3D
image, and refer to our method as the voxelated CNN (VCNN). The convolutional
layers automatically integrate interaction terms in the regressor; thus, no
explicit definition of clusters is required. As a model system, we combine our
VCNN potential with Monte Carlo simulations on a Ni$_{1-x}$Al$_x$ ($x$ < 30%)
and predict a disordered-to-ordered phase transition with less than 1 meV/atom
error. We also predict the energetic landscape of vacancy diffusion.
Classification of formation energy with respect to short-range-ordering of Al
alloys around a vacancy reveals that the ordering decreases the probability of
Ni diffusion. As the width of our input layer does not depend on the atomic
composition, VCNNs can be applied to study alloys with arbitrary numbers of
elements and empty lattice sites, without additional computational costs.
