  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.
