The Falicov-Kimball (FK) model was initially introduced as a statistic
al model for metal-insulator transition in correlated electron systems. It
can be exactly solved by combining the classical Monte Carlo method for t
he lattice gas and exact diagonalization (ED) for the itinerant electrons.
However\, direct ED calculation\, which is required in each time-step of
dynamical simulations of the FK model\, is very time-consuming. Here we ap
ply the modern machine learning (ML) technique to enable the first-ever la
rge-scale kinetic Monte Carlo (kMC) simulations of FK model. Using our neu
ral-network model on a system of unprecedented 10^{5} lattice site
s\, we uncover an intriguing hidden sub-lattice symmetry breaking in the p
hase separation dynamics of FK model.