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

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.

References in corpus (6)

• Ab initio theory and modeling of water
• Pure density functional for strong correlations and the thermodynamic limit from machine learning
• Gedanken Densities and Exact Constraints in Density Functional Theory
• Deorbitalization strategies for meta-GGA exchange-correlation functionals
• Accurate and numerically efficient r${}^2$SCAN meta-generalized gradient approximation
• Nonempirical Density Functionals Investigated for Jellium: Spin-Polarized Surfaces, Spherical Clusters, and Bulk Linear Response

Cited by in corpus (4)

• DeePKS+ABACUS as a Bridge between Expensive Quantum Mechanical Models and Machine Learning Potentials
• Artificial Intelligence for Science in Quantum, Atomistic, and Continuum Systems
• The Convexity Condition of Density-Functional Theory
• Exchange-Correlation Functionals in 2D Materials: Applications, Challenges, and Limitations