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

TL;DR

The work tackles the computational bottleneck of real-time TDDFT by learning autoregressive Fourier neural operators that propagate the electron density directly from past density histories and time-dependent fields. By incorporating physics-informed losses and multiple input representations, the approach achieves accurate, stable density rollouts with millisecond per-step inference, outperforming coarse traditional solvers on a 1D diatomic model. The study demonstrates generalization to higher spatial resolution and longer time horizons, preserves key observables such as the dipole moment, and enforces particle-number conservation, suggesting practical utility for rapid parameter sweeps and on-the-fly simulations. While limited to 1D ALDA TDDFT, the methodology offers a blueprint for extending to 3D and more complex dynamics, potentially enabling on-demand simulation and control of laser-driven electronic processes.

Abstract

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.

Figures (6)

• Figure 1: Autoregressive FNO architecture for predicting the density at time $t+1$ based on $k$ previous time steps.
• Figure 2: Results for a representative system.
• Figure 3: Observables calculated for the representative system. Left: Dipole moment calculated from reference and predicted density. Right: Total TF energy calculated from reference and predicted density.
• Figure 4: Integrated density over time for predicted rollouts. The conservation loss keeps particle number near 2 throughout.
• Figure 5: Results for the time reversed representative system.