  We demonstrate machine-learning enabled large-scale dynamical simulations of
electronic phase separation in double-exchange system. This model, also known
as the ferromagnetic Kondo lattice model, is believed to be relevant for the
colossal magnetoresistance phenomenon. Real-space simulations of such
inhomogeneous states with exchange forces computed from the electron
Hamiltonian can be prohibitively expensive for large systems. Here we show that
linear-scaling exchange field computation can be achieved using neural networks
trained by datasets from exact calculation on small lattices. Our
Landau-Lifshitz dynamics simulations based on machine-learning potentials
nicely reproduce not only the nonequilibrium relaxation process, but also
correlation functions that agree quantitatively with exact simulations. Our
work paves the way for large-scale dynamical simulations of correlated electron
systems using machine-learning models.
