# Heat flux for semi-local machine-learning potentials

arXiv: https://arxiv.org/abs/2303.14434 · HTML: https://mlsanity.com/paper/2303.14434/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 68 references that are in the map.
- First posted on arXiv 25 Mar 2023.

## Builds on (most cited first, 8 of 8)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields](https://mlsanity.com/paper/2206.07697/) (2022)
- [Equivariant message passing for the prediction of tensorial properties and molecular spectra](https://mlsanity.com/paper/2102.03150/) (2021)
- [Machine Learning Force Fields](https://mlsanity.com/paper/2010.07067/) (2020)
- [SpookyNet: Learning Force Fields with Electronic Degrees of Freedom and Nonlocal Effects](https://mlsanity.com/paper/2105.00304/) (2021)
- [The Design Space of E(3)-Equivariant Atom-Centered Interatomic Potentials](https://mlsanity.com/paper/2205.06643/) (2022)
- [Accurate Machine Learned Quantum-Mechanical Force Fields for Biomolecular Simulations](https://mlsanity.com/paper/2205.08306/) (2022)

## Built on by (most cited first, 3 of 3)

- [Stress and heat flux via automatic differentiation](https://mlsanity.com/paper/2305.01401/) (2023)
- [From Peptides to Nanostructures: A Euclidean Transformer for Fast and Stable Machine Learned Force Fields](https://mlsanity.com/paper/2309.15126/) (2023)
- [Accelerating the Training and Improving the Reliability of Machine-Learned Interatomic Potentials for Strongly Anharmonic Materials through Active Learning](https://mlsanity.com/paper/2409.11808/) (2024)

## Abstract (arXiv)

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.