We present a scalable machine learning (ML) framework for large-scale kinetic Monte Carlo (kMC) simulations of itinerant electron Ising systems. As the effective interactions between Ising spins in such itinerant magnets are mediated by conducting electrons, the calculation of energy change due to a local spin update requires solving an electronic structure problem. Such repeated electronic structure calculations could be overwhelmingly prohibitive for large systems. Assuming the locality principle, a convolutional neural network (CNN) model is developed to directly predict the effective local field and the corresponding energy change associated with a given spin update based on Ising configuration in a finite neighborhood. As the kernel size of the CNN is fixed at a constant, the model can be directly scalable to kMC simulations of large lattices. Our approach is reminiscent of the ML force-field models widely used in first-principles molecular dynamics simulations. Applying our ML framework to a square-lattice double-exchange Ising model, we uncover unusual coarsening of ferromagnetic domains at low temperatures. Our work highlights the potential of ML methods for large-scale modeling of similar itinerant systems with discrete dynamical variables.

翻译：我们提出了一种可扩展的机器学习框架，用于巡游电子伊辛系统的大规模动力学蒙特卡洛模拟。在此类巡游磁体中，伊辛自旋间的有效相互作用由传导电子作为媒介，因此计算局部自旋更新导致的能量变化需要求解电子结构问题。对于大体系而言，这类重复的电子结构计算可能因计算量过大而无法实现。基于局域性原理，我们开发了一种卷积神经网络模型，该模型能够根据有限邻域内的伊辛构型，直接预测给定自旋更新所对应的有效局域场及其能量变化。由于CNN的卷积核尺寸固定为常数，该模型可直接扩展至大晶格的kMC模拟。我们的方法类似于第一性原理分子动力学模拟中广泛使用的机器学习力场模型。将本ML框架应用于方格晶格双交换伊辛模型后，我们发现了低温下铁磁畴不寻常的粗化现象。本研究凸显了机器学习方法在具有离散动力学变量的类似巡游体系大规模建模中的应用潜力。