# Stress and heat flux via automatic differentiation

arXiv: https://arxiv.org/abs/2305.01401 · HTML: https://mlsanity.com/paper/2305.01401/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 95 references that are in the map.
- First posted on arXiv 2 May 2023.

## Builds on (most cited first, 19 of 19)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [SchNet: A continuous-filter convolutional neural network for modeling quantum interactions](https://mlsanity.com/paper/1706.08566/) (2017)
- [Directional Message Passing for Molecular Graphs](https://mlsanity.com/paper/2003.03123/) (2020)
- [MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields](https://mlsanity.com/paper/2206.07697/) (2022)
- [Machine Learning Force Fields](https://mlsanity.com/paper/2010.07067/) (2020)
- [Machine learning for molecular simulation](https://mlsanity.com/paper/1911.02792/) (2019)
- [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)
- [So3krates: Equivariant attention for interactions on arbitrary length-scales in molecular systems](https://mlsanity.com/paper/2205.14276/) (2022)
- [SchNetPack 2.0: A neural network toolbox for atomistic machine learning](https://mlsanity.com/paper/2212.05517/) (2022)
- [Hyperactive Learning (HAL) for Data-Driven Interatomic Potentials](https://mlsanity.com/paper/2210.04225/) (2022)
- [Representations of molecules and materials for interpolation of quantum-mechanical simulations via machine learning](https://mlsanity.com/paper/2003.12081/) (2020)
- [Accurate Machine Learned Quantum-Mechanical Force Fields for Biomolecular Simulations](https://mlsanity.com/paper/2205.08306/) (2022)
- [Algorithmic Differentiation for Automated Modeling of Machine Learned Force Fields](https://mlsanity.com/paper/2208.12104/) (2022)
- [Heat flux for semi-local machine-learning potentials](https://mlsanity.com/paper/2303.14434/) (2023)

## Built on by (most cited first, 1 of 1)

- [From Peptides to Nanostructures: A Euclidean Transformer for Fast and Stable Machine Learned Force Fields](https://mlsanity.com/paper/2309.15126/) (2023)

## Abstract (arXiv)

Machine-learning potentials provide computationally efficient and accurate approximations of the Born-Oppenheimer potential energy surface. This potential determines many materials properties and simulation techniques usually require its gradients, in particular forces and stress for molecular dynamics, and heat flux for thermal transport properties. Recently developed potentials feature high body order and can include equivariant semi-local interactions through message-passing mechanisms. Due to their complex functional forms, they rely on automatic differentiation (AD), overcoming the need for manual implementations or finite-difference schemes to evaluate gradients. This study demonstrates a unified AD approach to obtain forces, stress, and heat flux for such potentials, and provides a model-independent implementation. The method is tested on the Lennard-Jones potential, and then applied to predict cohesive properties and thermal conductivity of tin selenide using an equivariant message-passing neural network potential.