Machine-Learning-Based Exchange-Correlation Functional with Physical Asymptotic Constraints

TL;DR

This paper introduces a neural network-based exchange-correlation functional for density functional theory that satisfies physical asymptotic constraints, leading to improved accuracy and generalization across diverse materials.

Contribution

It presents a novel ML model architecture that enforces asymptotic constraints, enhancing the physical reliability and applicability of ML-based functionals in electronic structure calculations.

Findings

Functional satisfies physical asymptotic constraints

Achieves higher accuracy than existing functionals

Effective across diverse materials with different electronic properties

Abstract

Density functional theory is the standard theory for computing the electronic structure of materials, which is based on a functional that maps the electron density to the energy. However, a rigorous form of the functional is not known and has been heuristically constructed by interpolating asymptotic constraints known for extreme situations, such as isolated atoms and uniform electron gas. Recent studies have demonstrated that the functional can be effectively approximated using machine learning (ML) approaches. However, most ML models do not satisfy asymptotic constraints. In this study, by applying a novel ML model architecture, we demonstrate a neural network-based exchange-correlation functional satisfying physical asymptotic constraints. Calculations reveal that the trained functional is applicable to various materials with an accuracy higher than that of existing functionals, even for materials whose electronic properties are different from the properties of materials in the training dataset. Our proposed approach thus improves the accuracy and generalization performance of the ML-based functional by combining the advantages of ML and analytical modeling.