Heat flux for semi-local machine-learning potentials

Abstract

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.

arXiv comment6 pages, 3 figures, excluding supplement (12 pages, 10 figures), v2: fixed figures. Additional information at https://marcel.science/gknet

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• Molecular dynamics simulations of heat transport using machine-learned potentials: A mini review and tutorial on GPUMD with neuroevolution potentials
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• Stress and heat flux via automatic differentiation
• Thermal conductivity of Li${}_3$PS${}_4$ solid electrolytes with ab initio accuracy
• Revisit Many-body Interaction Heat Current and Thermal Conductivity Calculation in Moment Tensor Potential/LAMMPS Interface