Neural-network Kohn-Sham exchange-correlation potential and its out-of-training transferability

TL;DR

This paper introduces a neural-network approach to approximate the Kohn-Sham exchange-correlation potential, demonstrating transferability and accuracy beyond training data, and offering a new pathway for efficient density functional calculations.

Contribution

It develops a neural-network scheme to predict the Kohn-Sham potential from charge density, enabling energy evaluation without explicit exchange-correlation formulas, and studies transferability limits.

Findings

Neural-network $V_{Hxc}$ accurately predicts charge density and energy outside training range.

Transferability is limited by model parameter boundaries, which can be mitigated.

The approach suggests a new efficient method for Kohn-Sham potential computation.

Abstract

We incorporate in the Kohn-Sham self consistent equation a trained neural-network projection from the charge density distribution to the Hartree-exchange-correlation potential $n \rightarrow V_{\rm Hxc}$ for possible numerical approach to the exact Kohn-Sham scheme. The potential trained through a newly developed scheme enables us to evaluate the total energy without explicitly treating the formula of the exchange-correlation energy. With a case study of a simple model we show that the well-trained neural-network $V_{\rm Hxc}$ achieves accuracy for the charge density and total energy out of the model parameter range used for the training, indicating that the property of the elusive ideal functional form of $V_{\rm Hxc}$ can approximately be encapsulated by the machine-learning construction. We also exemplify a factor that crucially limits the transferability--the boundary in the model parameter space where the number of the one-particle bound states changes--and see that this is cured by setting the training parameter range across that boundary. The training scheme and insights from the model study apply to more general systems, opening a novel path to numerically efficient Kohn-Sham potential.