Physics-informed Bayesian inference of external potentials in classical density-functional theory
File(s)
Published version
Author(s)
Malpica-Morales, Antonio
Yatsyshin, Peter
Duran-Olivencia, Miguel A
Kalliadasis, Serafim
Type
Journal Article
Abstract
The swift progression and expansion of machine learning (ML) have not gone unnoticed within the realm of statistical mechanics. In particular, ML techniques have attracted attention by the classical density-functional theory (DFT) community, as they enable automatic discovery of free-energy functionals to determine the equilibrium-density profile of a many-particle system. Within classical DFT, the external potential accounts for the interaction of the many-particle system with an external field, thus, affecting the density distribution. In this context, we introduce a statistical-learning framework to infer the external potential exerted on a classical many-particle system. We combine a Bayesian inference approach with the classical DFT apparatus to reconstruct the external potential, yielding a probabilistic description of the external-potential functional form with inherent uncertainty quantification. Our framework is exemplified with a grand-canonical one-dimensional classical particle ensemble with excluded volume interactions in a confined geometry. The required training dataset is generated using a Monte Carlo (MC) simulation where the external potential is applied to the grand-canonical ensemble. The resulting particle coordinates from the MC simulation are fed into the learning framework to uncover the external potential. This eventually allows us to characterize the equilibrium density profile of the system by using the tools of DFT. Our approach benchmarks the inferred density against the exact one calculated through the DFT formulation with the true external potential. The proposed Bayesian procedure accurately infers the external potential and the density profile. We also highlight the external-potential uncertainty quantification conditioned on the amount of available simulated data. The seemingly simple case study introduced in this work might serve as a prototype for studying a wide variety of applications, including adsorption, wetting, and capillarity, to name a few.
Date Issued
2023-09-14
Date Acceptance
2023-06-08
Citation
Journal of Chemical Physics, 2023, 159 (10)
ISSN
0021-9606
Publisher
American Institute of Physics
Journal / Book Title
Journal of Chemical Physics
Volume
159
Issue
10
Copyright Statement
© 2023 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
License URL
Identifier
https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:001068517200005&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=a2bf6146997ec60c407a63945d4e92bb
Subjects
Chemistry
Chemistry, Physical
HARD-SPHERE FLUID
INTERFACE
MONTE-CARLO
Physical Sciences
Physics
Physics, Atomic, Molecular & Chemical
Science & Technology
WALL
Publication Status
Published
Coverage Spatial
United States
Article Number
104109
Date Publish Online
2023-09-13