Statistical learning method for predicting density-matrix based electron dynamics

TL;DR

This paper introduces a statistical learning approach to infer molecular Hamiltonians from electron density time-series, enabling accurate prediction of electron dynamics in various scenarios, including unseen field conditions.

Contribution

The method extends previous work by scaling to larger molecules and integrating physical constraints and regularization to improve Hamiltonian learning and electron dynamics prediction.

Findings

Accurate prediction of electron density dynamics in field-free conditions.

Successful generalization to field-on scenarios outside training data.

Close quantitative agreement with ground truth simulations.

Abstract

We develop a statistical method to learn a molecular Hamiltonian matrix from a time-series of electron density matrices. We extend our previous method to larger molecular systems by incorporating physical properties to reduce dimensionality, while also exploiting regularization techniques like ridge regression for addressing multicollinearity. With the learned Hamiltonian we can solve the Time-Dependent Hartree-Fock (TDHF) equation to propagate the electron density in time, and predict its dynamics for field-free and field-on scenarios. We observe close quantitative agreement between the predicted dynamics and ground truth for both field-off trajectories similar to the training data, and field-on trajectories outside of the training data.