The Green-Kubo (GK) method is a rigorous framework for heat transport simulations in materials. However, it requires an accurate description of the potential-energy surface and carefully converged statistics. Machine-learning potentials can achieve the accuracy of first-principles simulations while allowing to reach well beyond their simulation time and length scales at a fraction of the cost. In this paper, we explain how to apply the GK approach to the recent class of message-passing machine-learning potentials, which iteratively consider semi-local interactions beyond the initial interaction cutoff. We derive an adapted heat flux formulation that can be implemented using automatic differentiation without compromising computational efficiency. The approach is demonstrated and validated by calculating the thermal conductivity of zirconium dioxide across temperatures.

翻译：格林-久保（GK）方法是材料热输运模拟的严格理论框架。然而，该方法需要精确描述势能面并谨慎收敛统计结果。机器学习势能以极低的计算成本超越第一性原理模拟的时空尺度，同时保持其精度。本文阐述了如何将GK方法应用于最近发展出的消息传递类机器学习势，该类势能通过迭代方式超越初始截断半径，考虑半局部相互作用。我们推导出适用于自动微分实现的热流公式，且不牺牲计算效率。通过计算二氧化锆在不同温度下的热导率，验证并展示了该方法的有效性。