Learning Neural Free-Energy Functionals with Pair-Correlation Matching

TL;DR

This paper presents a neural network approach to approximate the Helmholtz free-energy functional in density functional theory, trained solely on radial distribution functions, enabling accurate predictions of inhomogeneous densities in complex systems.

Contribution

Introduces a neural network method for learning the free-energy functional from radial distribution functions, avoiding costly sampling of external potentials.

Findings

Accurately predicts inhomogeneous density profiles in Lennard-Jones systems.

Circumvents the need for sampling heterogeneous density profiles.

Demonstrates effectiveness in complex external potentials.

Abstract

The intrinsic Helmholtz free-energy functional, the centerpiece of classical density functional theory, is at best only known approximately for 3D systems. Here we introduce a method for learning a neuralnetwork approximation of this functional by exclusively training on a dataset of radial distribution functions, circumventing the need to sample costly heterogeneous density profiles in a wide variety of external potentials. For a supercritical Lennard-Jones system with planar symmetry, we demonstrate that the learned neural free-energy functional accurately predicts inhomogeneous density profiles under various complex external potentials obtained from simulations.