# Machine Learning Time Propagators for Time-Dependent Density Functional Theory Simulations

arXiv: https://arxiv.org/abs/2508.16554 · HTML: https://mlsanity.com/paper/2508.16554/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 64 references that are in the map.
- First posted on arXiv 22 Aug 2025.

## Builds on (most cited first, 14 of 14)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Neural Operator: Graph Kernel Network for Partial Differential Equations](https://mlsanity.com/paper/2003.03485/) (2020)
- [Geometry-Informed Neural Operator for Large-Scale 3D PDEs](https://mlsanity.com/paper/2309.00583/) (2023)
- [Neural Operators for Accelerating Scientific Simulations and Design](https://mlsanity.com/paper/2309.15325/) (2023)
- [By-passing the Kohn-Sham equations with machine learning](https://mlsanity.com/paper/1609.02815/) (2016)
- [Solid Harmonic Wavelet Scattering for Predictions of Molecule Properties](https://mlsanity.com/paper/1805.00571/) (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)
- [Accelerating Finite-temperature Kohn-Sham Density Functional Theory with Deep Neural Networks](https://mlsanity.com/paper/2010.04905/) (2020)
- [Learning the electronic density of states in condensed matter](https://mlsanity.com/paper/2006.11803/) (2020)
- [Neural Quantum Propagators for Driven-Dissipative Quantum Dynamics](https://mlsanity.com/paper/2410.16091/) (2024)
- [Accelerating Electronic Stopping Power Predictions by 10 Million Times with a Combination of Time-Dependent Density Functional Theory and Machine Learning](https://mlsanity.com/paper/2311.00787/) (2023)
- [Accelerating Electron Dynamics Simulations through Machine Learned Time Propagators](https://mlsanity.com/paper/2407.09628/) (2024)
- [Materials Learning Algorithms (MALA): Scalable Machine Learning for Electronic Structure Calculations in Large-Scale Atomistic Simulations](https://mlsanity.com/paper/2411.19617/) (2024)
- [Scalable learning of potentials to predict time-dependent Hartree-Fock dynamics](https://mlsanity.com/paper/2408.04765/) (2024)

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

- [Orbital Transformers for Predicting Wavefunctions in Time-Dependent Density Functional Theory](https://mlsanity.com/paper/2603.03511/) (2026)

## Abstract (arXiv)

Time-dependent density functional theory (TDDFT) is a widely used method to investigate electron dynamics under external time-dependent perturbations such as laser fields. In this work, we present a machine learning approach to accelerate electron dynamics simulations based on real time TDDFT using autoregressive neural operators as time-propagators for the electron density. By leveraging physics-informed constraints and featurization, and high-resolution training data, our model achieves superior accuracy and computational speed compared to traditional numerical solvers. We demonstrate the effectiveness of our model on a class of one-dimensional diatomic molecules under the influence of a range of laser parameters. This method has potential in enabling on-the-fly modeling of laser-irradiated molecules and materials by utilizing fast machine learning predictions in a large space of varying experimental parameters of the laser.