Heat flux for semi-local machine-learning potentials

TL;DR

This paper adapts the Green-Kubo method for semi-local message-passing machine-learning potentials to accurately compute thermal conductivity, demonstrating its effectiveness on zirconium dioxide.

Contribution

It introduces a new heat flux formulation compatible with message-passing potentials and applies it to thermal conductivity calculations.

Findings

Accurately computes thermal conductivity of zirconium dioxide.

Validates the adapted Green-Kubo approach with machine-learning potentials.

Demonstrates efficiency and accuracy of the method.

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.