Neural network interpolation of exchange-correlation functional

TL;DR

This paper introduces neural network-based exchange-correlation functionals for density functional theory, demonstrating their ability to accurately reproduce traditional functionals and generalize to unseen systems, potentially surpassing existing methods.

Contribution

The authors develop neural network-based XC functionals that can accurately model DFT exchange-correlation effects and generalize well to new systems, offering a flexible alternative to traditional parametrizations.

Findings

NN XC functionals accurately reproduce LDA and GGA results

The local environment can be incorporated by adjusting NN architecture

NN functionals show good generalization to unseen systems

Abstract

Density functional theory (DFT) is one of the most widely used tools to solve the many-body Schrodinger equation. The core uncertainty inside DFT theory is the exchange-correlation (XC) functional, the exact form of which is still unknown. Therefore, the essential part of DFT success is based on the progress in the development of XC approximations. Traditionally, they are built upon analytic solutions in low- and high-density limits and result from quantum Monte Carlo numerical calculations. However, there is no consistent and general scheme of XC interpolation and functional representation. Many different developed parametrizations mainly utilize a number of phenomenological rules to construct a specific XC functional. In contrast, the neural network (NN) approach can provide a general way to parametrize an XC functional without any a priori knowledge of its functional form. In this work, we develop NN XC functionals and prove their applicability to 3-dimensional physical systems. We show that both the local density approximation (LDA) and generalized gradient approximation (GGA) are well reproduced by the NN approach. It is demonstrated that the local environment can be easily considered by changing only the number of neurons in the first layer of the NN. The developed NN XC functionals show good results when applied to systems that are not presented in the training/test data. The generalizability of the formulated NN XC framework leads us to believe that it could give superior results in comparison with traditional XC schemes provided training data from high-level theories such as the quantum Monte Carlo and post-Hartree-Fock methods.