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 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 machine learning 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.

翻译：非平衡电子力在电压驱动的相变中起着核心作用，但在动力学模拟中其计算成本极高。本文针对耦合非平衡电子的绝热晶格动力学开发了一个机器学习框架，并以Holstein模型中栅压诱导的电荷密度波态绝缘体-金属转变为例进行演示。虽然精确的电子力可通过非平衡格林函数（NEGF）计算获得，但其高昂的计算成本使得长时间动力学模拟难以实现。通过利用电子响应的局域性，我们训练了一个神经网络直接从晶格构型预测瞬时局域电子力，从而避免了时间演化过程中重复的NEGF计算。当与布朗动力学结合时，所得机器学习力场在定量重现完整NEGF模拟获得的畴壁运动和非平衡相变动力学的同时，实现了数个数量级的计算效率提升。我们的研究确立了直接力学习作为一种高效精确的方法，可用于模拟驱动量子材料中的非平衡晶格动力学。