Enabling ab initio configurational sampling of multicomponent solids with long-range interactions using neural network potentials and active learning.

We propose a scheme for ab initio configurational sampling in multicomponent crystalline solids using Behler-Parinello type neural network potentials (NNPs) in an unconventional way: the NNPs are trained to predict the energies of relaxed structures from the perfect lattice with configurational disorder instead of the usual way of training to predict energies as functions of continuous atom coordinates. Training set bias is avoided through an active learning scheme. This idea is demonstrated on the calculation of the temperature dependence of the degree of A/B site inversion in MgAl$_2$O$_4$, which is a multivalent system requiring careful handling of long-range interactions. The present scheme may serve as an alternative to cluster expansion for `difficult' systems, e.g., complex bulk or interface systems with many components and sublattices that are relevant to many technological applications today.