We review recent advances in machine learning (ML) force-field methods for Landau-Lifshitz-Gilbert (LLG) simulations of itinerant electron magnets, focusing on scalability and transferability. Built on the principle of locality, a deep neural network model is developed to efficiently and accurately predict the electron-mediated forces governing spin dynamics. Symmetry-aware descriptors constructed through a group-theoretical approach ensure rigorous incorporation of both lattice and spin-rotation symmetries. The framework is demonstrated using the prototypical s-d exchange model widely employed in spintronics. ML-enabled large-scale simulations reveal novel nonequilibrium phenomena, including anomalous coarsening of tetrahedral spin order on the triangular lattice and the freezing of phase separation dynamics in lightly hole-doped, strong-coupling square-lattice systems. These results establish ML force-field frameworks as scalable, accurate, and versatile tools for modeling nonequilibrium spin dynamics in itinerant magnets.

翻译：本文综述了机器学习力场方法在巡游电子磁体Landau-Lifshitz-Gilbert（LLG）模拟中的最新进展，重点关注方法的可扩展性与可迁移性。基于局域性原理，我们开发了一种深度神经网络模型，能够高效且精确地预测支配自旋动力学的电子介导力。通过群论方法构建的对称性感知描述符，确保了晶格对称性与自旋旋转对称性的严格融入。该框架以自旋电子学中广泛采用的典型s-d交换模型为例进行演示。基于机器学习的大规模模拟揭示了新颖的非平衡现象，包括三角晶格上四面体自旋序的异常粗化，以及轻空穴掺杂强耦合方晶格体系中相分离动力学的冻结。这些结果表明，机器学习力场框架是模拟巡游磁体中非平衡自旋动力学的可扩展、精确且多功能的工具。