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Determining the Chemical Potential via Universal Density Functional Learning

Florian Sammüller* and Matthias Schmidt†

  • *Contact author: florian.sammueller@uni-bayreuth.de
  • †Contact author: matthias.schmidt@uni-bayreuth.de
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Phys. Rev. Lett. 136, 068202 – Published 10 February, 2026

DOI: https://doi.org/10.1103/7bqn-y2d7

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.

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Phys. Rev. Lett. 136, 068202– Published 10 February, 2026
  • Received 18 June 2025
  • Accepted 23 December 2025
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