Exact constraints and appropriate norms in machine learned exchange-correlation functionals

TL;DR

This paper develops a deep neural network that incorporates exact constraints and norms to replicate and deorbitalize the SCAN functional, enhancing transferability for molecular and periodic systems.

Contribution

It introduces a novel machine learning approach that embeds exact constraints and norms to improve density functional approximations without relying on orbital-dependent data.

Findings

The neural network successfully replicates the SCAN functional.

The model demonstrates good transferability to molecular and periodic systems.

It avoids using orbital-dependent kinetic energy density.

Abstract

Machine learning techniques have received growing attention as an alternative strategy for developing general-purpose density functional approximations, augmenting the historically successful approach of human designed functionals derived to obey mathematical constraints known for the exact exchange-correlation functional. More recently efforts have been made to reconcile the two techniques, integrating machine learning and exact-constraint satisfaction. We continue this integrated approach, designing a deep neural network that exploits the exact constraint and appropriate norm philosophy to deorbitalize the strongly constrained and appropriately normed SCAN functional. The deep neural network is trained to replicate the SCAN functional from only electron density and local derivative information, avoiding use of the orbital dependent kinetic energy density. The performance and transferability of the machine learned functional are demonstrated for molecular and periodic systems.