Facilitating {\it ab initio} configurational sampling of multicomponent solids using an on-lattice neural network model and active learning

We propose a scheme for {\it 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. An active learning scheme is employed to obtain a training set containing configurations of thermodynamic relevance. This enables bypassing of the structural relaxation procedure which is necessary when applying conventional NNP approaches to the lattice configuration problem. The idea is demonstrated on the calculation of the temperature dependence of the degree of A/B site inversion in three spinel oxides, MgAl$_2$O$_4$, ZnAl$_2$O$_4$, and MgGa$_2$O$_4$. 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.