Metadensity functional theory for classical fluids: Extracting the pair potential

TL;DR

This paper introduces a machine learning approach using neural networks to accurately predict inhomogeneous states and invert structural data to obtain pair potentials in classical fluids, addressing a key challenge in liquid physics and soft matter design.

Contribution

A novel neural network-based metadensity functional for arbitrary pair potentials in classical fluids, enabling accurate predictions and inversion of structural data.

Findings

Accurate predictions for inhomogeneous states in 1D fluids

Immediate access to pair distribution functions

Effective inversion of structural data to pair potentials

Abstract

The excess free energy functional of classical density functional theory depends upon the type of fluid model, specifically on the choice of (pair) potential, is unknown in general, and is approximated reliably only in special cases. We present a machine learning scheme for training a neural network that acts as a generic metadensity functional for truncated but otherwise arbitrary pair potentials. Automatic differentiation and neural functional calculus then yield, for one-dimensional fluids, accurate predictions for inhomogeneous states and immediate access to the pair distribution function. The approach provides a means of addressing a fundamental problem in the physics of liquids, and for soft matter design: How best to invert structural data to obtain the pair potential?