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Updated: Jul 16, 2025

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
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Physics-informed Bayesian inference of external potentials in classical density-functional theory.

Antonio Malpica-Morales1, Peter Yatsyshin1,2, Miguel A Durán-Olivencia1,3

  • 1Department of Chemical Engineering, Imperial College, London SW7 2AZ, United Kingdom.

The Journal of Chemical Physics
|September 13, 2023
PubMed
Summary
This summary is machine-generated.

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This study introduces a machine learning framework to infer external potentials in statistical mechanics. The Bayesian approach accurately reconstructs potentials and density profiles, quantifying uncertainty for applications like adsorption and wetting.

Area of Science:

  • Statistical Mechanics
  • Machine Learning
  • Computational Physics

Background:

  • Machine learning (ML) is rapidly advancing, drawing interest from statistical mechanics and classical density-functional theory (DFT).
  • Classical DFT uses external potentials to influence many-particle systems and determine equilibrium density profiles.
  • Automatic discovery of free-energy functionals in DFT is a key challenge addressed by ML.

Purpose of the Study:

  • To develop a statistical-learning framework for inferring the external potential acting on a classical many-particle system.
  • To combine Bayesian inference with classical DFT for reconstructing external potentials and quantifying their uncertainty.
  • To validate the framework's accuracy in predicting system density profiles.

Main Methods:

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  • A Bayesian inference approach is integrated with classical DFT.
  • A Monte Carlo (MC) simulation generates training data by applying an external potential to a 1D classical particle ensemble.
  • The framework infers the external potential from particle coordinates obtained via MC simulation.

    • Main Results:

    • The proposed framework accurately infers the external potential and the equilibrium density profile.
    • Uncertainty quantification of the inferred external potential is achieved.
    • Performance is benchmarked against the exact density profile calculated using the true external potential.

    Conclusions:

    • The Bayesian statistical-learning framework effectively reconstructs external potentials and density profiles in classical DFT.
    • The method provides crucial uncertainty quantification, dependent on the volume of simulated data.
    • This work serves as a prototype for diverse applications, including adsorption, wetting, and capillarity phenomena.