Metadensity functional learning for classical fluids: Regularizing with pair correlations

TL;DR

This paper introduces a neural metadensity functional approach to model inhomogeneous fluids, enabling flexible pair potential adjustments and improved correlation structure predictions using functional differentiation and regularization techniques.

Contribution

It develops a novel neural functional framework that leverages pair potential dependence for more accurate and adaptable fluid structure modeling, surpassing traditional inversion methods.

Findings

Metadensity functional captures pair correlations effectively.

Regularization improves neural functional learning accuracy.

Method circumvents Ornstein-Zernike inversion using first-principles-based functional dependence.

Abstract

We investigate and exploit consequences of the recent neural metadensity functional theory [Kampa et al., Phys. Rev. Lett. 134, 107301 (2025), 10.1103/PhysRevLett.134.107301] for describing the physics of inhomogeneous fluids. The metadensity dependence on the pair potential is relevant for soft matter design and Henderson inversion and it allows one to change the pair potential on the fly at prediction stage. Here we consider one-dimensional systems with short-ranged (truncated) interparticle forces and draw on the functional pair potential dependence to investigate 'metadirect' routes towards the bulk fluid pair correlation structure. Classical density functional theory provides the required functional relationships. Efficient variational calculus is implemented by neural functional line integration and automatic differentiation. We regularize local learning of neural functionals by comparing the pair structure from different routes. Thereby results from metadirect functional differentiation are matched against accurate test particle data from an initial locally trained metadensity functional. Accessing the pair structure via the metadensity functional dependence circumvents Ornstein-Zernike inversion and it is based on first principles.