Bridging electronic and classical density-functional theory using universal machine-learned functional approximations

TL;DR

This paper introduces a universal machine learning framework for nonlocal density-functional approximations, unifying electronic and classical DFT approaches with promising accuracy across diverse 1D and quasi-1D systems.

Contribution

It develops a general ML-based approach combining equivariant CNNs and weighted-density approximation, enabling a single functional to accurately model both electronic and classical fluids.

Findings

Achieved high accuracy for various 1D and quasi-1D systems

Demonstrated the same hyperparameters work across different models

Laid groundwork for universal 3D density functional approximations

Abstract

The accuracy of density-functional theory (DFT) is determined by the quality of the approximate functionals, such as exchange-correlation in electronic DFT and the excess functional in the classical DFT formalism of fluids. The exact functional is highly nonlocal for both electrons and fluids, yet most approximate functionals are semi-local or nonlocal in a limited weighted-density form. Machine-learned (ML) nonlocal density-functional approximations are promising in both electronic and classical DFT, but have so far employed disparate approaches with limited generality. Here, we formulate a universal approximation framework and training protocol for nonlocal ML functionals, combining features of equivariant convolutional neural networks and the weighted-density approximation. We prototype this approach for several 1D and quasi-1D problems and demonstrate that a functional with exactly the same hyperparameters achieves excellent accuracy for the hard-rod fluid, the inhomogeneous Ising model, the exact exchange functional for electrons, the electron kinetic energy functional for orbital-free DFT, as well as for liquid water with 1D inhomogeneities. These results lay the foundation for a universal ML approach to exact 3D functionals spanning electronic and classical DFT.