Determining the chemical potential via universal density functional learning

TL;DR

This paper introduces a machine learning approach to determine the chemical potential in inhomogeneous classical fluids by learning density functionals, providing an efficient alternative to traditional methods and enabling multiscale predictions.

Contribution

The authors develop a neural network-based method to simultaneously learn the universal density functional and the chemical potential from simulation data.

Findings

Successfully determines chemical potential across datasets

Learns the universal density functional with neural networks

Offers an efficient alternative to conventional methods

Abstract

We demonstrate that the machine learning of density functionals allows one to determine simultaneously the equilibrium chemical potential across simulation datasets of inhomogeneous classical fluids. Minimization of a loss function based on an Euler-Lagrange equation yields both the universal one-body direct correlation functional, which is represented locally by a neural network, as well as the system-specific unknown chemical potential values. The method can serve as an efficient alternative to conventional computational techniques of measuring the chemical potential. It also facilitates using canonical data from Brownian dynamics, molecular dynamics, or Monte Carlo simulations as a basis for constructing neural density functionals, which are fit for accurate multiscale prediction of soft matter systems in equilibrium.