On-lattice voxelated convolutional neural networks for prediction of phase diagrams and diffusion barriers in cubic alloys
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.