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

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 de-orbitalize 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 the use of the orbital-dependent kinetic energy density. The performance and transferability of the machine-learned functional are demonstrated for molecular and periodic systems.

Automated summary

This study designs a deep neural network using machine learning techniques to replicate strongly constrained and appropriately normed functional by only using electron density and local derivative information. The experimental results demonstrate that this machine learning approach shows good performance and transferability in molecular and periodic systems.