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

TL;DR

This paper introduces a voxelated CNN (VCNN) approach for predicting phase diagrams and diffusion barriers in cubic alloys, offering improved accuracy over traditional cluster expansion methods by automatically capturing interaction terms.

Contribution

The novel VCNN method directly models on-lattice potentials on cubic sites, eliminating the need for explicit cluster definitions and enabling efficient analysis of multi-element alloys.

Findings

Achieved less than 1 meV/atom error in phase transition prediction.

Predicted vacancy diffusion landscape and effects of ordering.

Applicable to alloys with arbitrary element compositions without extra computational cost.

Abstract

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.