  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.
