Machine learning nonequilibrium phase transitions in charge-density wave insulators

Abstract Nonequilibrium electronic forces play a central role in voltage-driven phase transitions but are notoriously expensive to evaluate in dynamical simulations. Here we develop a machine-learning (ML) framework for adiabatic lattice dynamics coupled to nonequilibrium electrons, and demonstrate it for a gating-induced insulator-to-metal transition out of a charge-density-wave state in the Holstein model. Although exact electronic forces can be obtained from nonequilibrium Green’s-function (NEGF) calculations, their high computational cost renders long-time dynamical simulations prohibitively expensive. By exploiting the locality of the electronic response, we train a neural network to directly predict instantaneous local electronic forces from the lattice configuration, thereby bypassing repeated NEGF calculations during time evolution. When combined with Brownian dynamics, the resulting ML force field quantitatively reproduces domain-wall motion and nonequilibrium phase-transition dynamics obtained from full NEGF simulations, while achieving orders-of-magnitude gains in computational efficiency. Our results establish direct force learning as an efficient and accurate approach for simulating nonequilibrium lattice dynamics in driven quantum materials.