Green-Kubo Thermal Conductivities with Message-Passing Neural Networks

Accurate, precise, and efficient computational access to thermal conductivities of known and novel materials is a challenging and urgent problem that concerns scientific understanding as well as industrial applications. The Green-Kubo (GK) method combined with first-principles calculations enables the accurate determination of thermal conductivities, even for strongly anharmonic materials [1], but its applicability is limited by the high computational cost of the long dynamics simulations required. Machine-learning potentials can reduce this cost by orders of magnitude. Message-passing neural networks (MPNNs) acting on a graph representation of a material are promising for this application due to their relational inductive bias and implicit long-range nature. They model interactions between atoms as multiple iterations of a short-range interaction, allowing information to propagate beyond local environments while avoiding the costly evaluation of explicit long-range interactions. We show how the GK method can be formulated and implemented using MPNNs, and benchmark their performance for zirconium dioxide, a strongly anharmonic material.

[1]: C. Carbogno, R. Ramprasad, and M. Scheffler, Phys. Rev. Lett. 118 175901 (2017).