Machine-learning Kohn-Sham potential from dynamics in time-dependent Kohn-Sham systems

TL;DR

This paper introduces a machine learning approach to develop the Kohn-Sham potential in time-dependent density functional theory, improving the accuracy of modeling many-electron systems without requiring exact potential data.

Contribution

A novel machine learning method that constructs the time-dependent Kohn-Sham potential from system dynamics without needing exact potential training data.

Findings

Accurately reproduces the exact Kohn-Sham potential in simple systems

Captures system dynamics even with memory effects

Provides insights for better functional approximations

Abstract

The construction of a better exchange-correlation potential in time-dependent density functional theory (TDDFT) can improve the accuracy of TDDFT calculations and provide more accurate predictions of the properties of many-electron systems. Here, we propose a machine learning method to develop the energy functional and the Kohn-Sham potential of a time-dependent Kohn-Sham system is proposed. The method is based on the dynamics of the Kohn-Sham system and does not require any data on the exact Kohn-Sham potential for training the model. We demonstrate the results of our method with a 1D harmonic oscillator example and a 1D two-electron example. We show that the machine-learned Kohn-Sham potential matches the exact Kohn-Sham potential in the absence of memory effect. Our method can still capture the dynamics of the Kohn-Sham system in the presence of memory effects. The machine learning method developed in this article provides insight into making better approximations of the energy functional and the Kohn-Sham potential in the time-dependent Kohn-Sham system.