# Machine learning nonequilibrium electron forces for adiabatic spin dynamics

arXiv: https://arxiv.org/abs/2112.12124 · HTML: https://mlsanity.com/paper/2112.12124/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 106 references that are in the map.
- First posted on arXiv 22 Dec 2021.

## Builds on (most cited first, 12 of 12)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Deep Potential Molecular Dynamics: a scalable model with the accuracy of quantum mechanics](https://mlsanity.com/paper/1707.09571/) (2017)
- [Continuously Differentiable Exponential Linear Units](https://mlsanity.com/paper/1704.07483/) (2017)
- [Unifying machine learning and quantum chemistry -- a deep neural network for molecular wavefunctions](https://mlsanity.com/paper/1906.10033/) (2019)
- [By-passing the Kohn-Sham equations with machine learning](https://mlsanity.com/paper/1609.02815/) (2016)
- [Machine Learning for Condensed Matter Physics](https://mlsanity.com/paper/2005.14228/) (2020)
- [Accelerate Monte Carlo Simulations with Restricted Boltzmann Machines](https://mlsanity.com/paper/1610.02746/) (2016)
- [Machine learning dynamics of phase separation in correlated electron magnets](https://mlsanity.com/paper/2006.04205/) (2020)
- [Anomalous phase separation dynamics in a correlated electron system: machine-learning enabled large-scale kinetic Monte Carlo simulations](https://mlsanity.com/paper/2105.13304/) (2021)
- [Machine learning electron correlation in a disordered medium](https://mlsanity.com/paper/1810.02323/) (2018)
- [Quantum deep field: data-driven wave function, electron density generation, and atomization energy prediction and extrapolation with machine learning](https://mlsanity.com/paper/2011.07923/) (2020)
- [Modeling Tangential Vector Fields on a Sphere](https://mlsanity.com/paper/1612.08062/) (2016)

## Built on by (most cited first, 17 of 17)

- [Machine learning for phase ordering dynamics of charge density waves](https://mlsanity.com/paper/2303.03493/) (2023)
- [Coarsening of chiral domains in itinerant electron magnets: A machine learning force field approach](https://mlsanity.com/paper/2403.11705/) (2024)
- [Kinetics of orbital ordering in cooperative Jahn-Teller models: Machine-learning enabled large-scale simulations](https://mlsanity.com/paper/2405.14776/) (2024)
- [Machine learning force-field model for kinetic Monte Carlo simulations of itinerant Ising magnets](https://mlsanity.com/paper/2411.19780/) (2024)
- [Machine-learning force-field models for dynamical simulations of metallic magnets](https://mlsanity.com/paper/2602.18213/) (2026)
- [Graph Neural Networks in the Wilson Loop Representation of Abelian Lattice Gauge Theories](https://mlsanity.com/paper/2605.03901/) (2026)
- [Equivariant Neural Networks for Spin Dynamics Simulations of Itinerant Magnets](https://mlsanity.com/paper/2305.03804/) (2023)
- [Machine learning force-field models for metallic spin glass](https://mlsanity.com/paper/2311.16964/) (2023)
- [Echo State network for coarsening dynamics of charge density waves](https://mlsanity.com/paper/2412.11982/) (2024)
- [Machine learning nonequilibrium phase transitions in charge-density wave insulators](https://mlsanity.com/paper/2601.07583/) (2026)
- [Graph neural network force fields for adiabatic dynamics of lattice Hamiltonians](https://mlsanity.com/paper/2603.02039/) (2026)
- [Machine-learning modeling of magnetization dynamics in quasi-equilibrium and driven metallic spin systems](https://mlsanity.com/paper/2604.11513/) (2026)
- [Machine learning approach for vibronically renormalized electronic band structures](https://mlsanity.com/paper/2409.01523/) (2024)
- [Enhanced coarsening of charge density waves induced by electron correlation: Machine-learning enabled large-scale dynamical simulations](https://mlsanity.com/paper/2412.21072/) (2024)
- [Learning Degenerate Manifolds of Frustrated Magnets with Boltzmann Machines](https://mlsanity.com/paper/2511.19879/) (2025)
- [Magnetic HIP-NN for spin dynamics in disordered itinerant magnets](https://mlsanity.com/paper/2606.10349/) (2026)
- [Graph Neural Network Force Fields for Spin Dynamics in Metallic Magnets](https://mlsanity.com/paper/2607.28537/) (2026)

## Abstract (arXiv)

We present a generalized potential theory of nonequilibrium torques for the Landau-Lifshitz equation. The general formulation of exchange forces in terms of two potential energies allows for the implementation of accurate machine learning models for adiabatic spin dynamics of out-of-equilibrium itinerant magnetic systems. To demonstrate our approach, we develop a deep-learning neural network that successfully learns the forces in a driven s-d model computed from the nonequilibrium Green's function method. We show that the Landau-Lifshitz dynamics simulations with forces predicted from the neural-net model accurately reproduce the voltage-driven domain-wall propagation. Our work opens a new avenue for multi-scale modeling of nonequilibrium dynamical phenomena in itinerant magnets and spintronics based on machine-learning models.