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Accelerating Electron Dynamics Simulations through Machine Learned Time Propagators

Karan Shah, Attila Cangi

TL;DR

The paper addresses the computational bottleneck of real-time TDDFT by replacing orbital-temporal propagation with autoregressive Fourier neural operators that directly evolve the electron density $n(\mathbf{r},t)$. By integrating physics-informed constraints and an autoregressive density predictor based on Fourier neural operators, the approach achieves faster inference and competitive accuracy on 1D diatomic models under laser perturbations, compared to conventional Crank-Nicolson-based solvers. Key contributions include formulating an autoregressive FNO propagator for TDDFT densities, demonstrating discretization-invariant super-resolution behavior, and validating robustness to time-grid offsets. The work holds potential for on-the-fly, parameter-aware simulations in laser-m driven electron dynamics, with future extensions to 3D enabling real-time modeling for experimental setups and quantum control applications.

Abstract

Time-dependent density functional theory (TDDFT) is a widely used method to investigate electron dynamics under various external perturbations such as laser fields. In this work, we present a novel approach to accelerate real time TDDFT based electron dynamics simulations using autoregressive neural operators as time-propagators for the electron density. By leveraging physics-informed constraints 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. This method has potential in enabling real-time, on-the-fly modeling of laser-irradiated molecules and materials with varying experimental parameters.

Accelerating Electron Dynamics Simulations through Machine Learned Time Propagators

TL;DR

The paper addresses the computational bottleneck of real-time TDDFT by replacing orbital-temporal propagation with autoregressive Fourier neural operators that directly evolve the electron density . By integrating physics-informed constraints and an autoregressive density predictor based on Fourier neural operators, the approach achieves faster inference and competitive accuracy on 1D diatomic models under laser perturbations, compared to conventional Crank-Nicolson-based solvers. Key contributions include formulating an autoregressive FNO propagator for TDDFT densities, demonstrating discretization-invariant super-resolution behavior, and validating robustness to time-grid offsets. The work holds potential for on-the-fly, parameter-aware simulations in laser-m driven electron dynamics, with future extensions to 3D enabling real-time modeling for experimental setups and quantum control applications.

Abstract

Time-dependent density functional theory (TDDFT) is a widely used method to investigate electron dynamics under various external perturbations such as laser fields. In this work, we present a novel approach to accelerate real time TDDFT based electron dynamics simulations using autoregressive neural operators as time-propagators for the electron density. By leveraging physics-informed constraints 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. This method has potential in enabling real-time, on-the-fly modeling of laser-irradiated molecules and materials with varying experimental parameters.
Paper Structure (15 sections, 23 equations, 3 figures, 1 table)

This paper contains 15 sections, 23 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Methods
  3. Time-Dependent Density Functional Theory
  4. Time Propagators
  5. Model Systems
  6. Fourier neural operators
  7. Modeling the time-dependent electron density with Fourier neural operators
  8. Results
  9. Effect of varying input time slice
  10. Comparison with coarse solver
  11. Time offset
  12. Spatial super-resolution
  13. Discussion
  14. Properties of time evolution operators
  15. Conclusion

Figures (3)

  • Figure 1: Example system with $d=1.0, Z_1=2.0, Z_2=4.0$. (a) Ground State Density, (b) Ground State Potentials, (c) Laser Field
  • Figure 2: Autoregressive FNO architecture for predicting the density at time $t+1$ based on $k$ previous time steps.
  • Figure 3: Density evolution of the representative system. The red line denotes the initial $T_{in}=10$ input time slices. The errors are calculated on the predicted density slices after the red line.