# Machine learning nonequilibrium phase transitions in charge-density wave insulators

arXiv: https://arxiv.org/abs/2601.07583 · HTML: https://mlsanity.com/paper/2601.07583/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 76 references that are in the map.
- First posted on arXiv 12 Jan 2026.

## Builds on (most cited first, 16 of 16)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [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)
- [DScribe: Library of Descriptors for Machine Learning in Materials Science](https://mlsanity.com/paper/1904.08875/) (2019)
- [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)
- [Machine learning nonequilibrium electron forces for adiabatic spin dynamics](https://mlsanity.com/paper/2112.12124/) (2021)
- [Descriptors for Machine Learning Model of Generalized Force Field in Condensed Matter Systems](https://mlsanity.com/paper/2201.00798/) (2022)
- [Machine learning predictions for local electronic properties of disordered correlated electron systems](https://mlsanity.com/paper/2204.05967/) (2022)
- [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)
- [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)

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

- [Graph neural network force fields for adiabatic dynamics of lattice Hamiltonians](https://mlsanity.com/paper/2603.02039/) (2026)

## Abstract (arXiv)

Nonequilibrium electronic forces play a central role in voltage-driven phase transitions but are notoriously expensive to evaluate in dynamical simulations. Here we develop a machine learning framework for adiabatic lattice dynamics coupled to nonequilibrium electrons, and demonstrate it for a gating induced insulator to metal transition out of a charge density wave state in the Holstein model. Although exact electronic forces can be obtained from nonequilibrium Green's function (NEGF) calculations, their high computational cost renders long time dynamical simulations prohibitively expensive. By exploiting the locality of the electronic response, we train a neural network to directly predict instantaneous local electronic forces from the lattice configuration, thereby bypassing repeated NEGF calculations during time evolution. When combined with Brownian dynamics, the resulting machine learning force field quantitatively reproduces domain wall motion and nonequilibrium phase transition dynamics obtained from full NEGF simulations, while achieving orders of magnitude gains in computational efficiency. Our results establish direct force learning as an efficient and accurate approach for simulating nonequilibrium lattice dynamics in driven quantum materials.