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Physics-constrained Bayesian inference of state functions in classical density-functional theory

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Title: Physics-constrained Bayesian inference of state functions in classical density-functional theory
Authors: Yatsyshin, P
Kalliadasis, S
Duncan, AB
Item Type: Journal Article
Abstract: We develop a novel data-driven approach to the inverse problem of classical statistical mechanics: given experimental data on the collective motion of a classical many-body system, how does one characterise the free energy landscape of that system? By combining non-parametric Bayesian inference with physically-motivated constraints, we develop an efficient learning algorithm which automates the construction of approximate free energy functionals. In contrast to optimisation-based machine learning approaches, which seek to minimise a cost function, the centralidea of the proposed Bayesian inference is to propagate a set of prior assumptions through the model, derived from physical principles. The experimental data is used to probabilistically weigh the possible model predictions. This naturally leads to humanly interpretable algorithms with full uncertainty quantification of predictions. In our case, the output of the learning algorithm is a probability distribution over a family of free energy functionals, consistent with the observed particle data. We find that surprisingly small data samples contain sufficient information for inferring highly accurate analytic expressions of the underlying free energy functionals, making our algorithm highly data efficient. We consider excluded volume particle interactions, which are ubiquitous in nature, whilst being highly challenging for modelling in terms of free energy. To validate our approach we consider the paradigmatic case of one-dimensional fluid and develop inference algorithms for the canonical and grand-canonical statistical-mechanical ensembles. Extensions to higher dimensional systems are conceptually straightforward, whilst standard coarse-graining techniques allow one to easily incorporate attractive interactions
Issue Date: 21-Feb-2022
Date of Acceptance: 13-Dec-2021
URI: http://hdl.handle.net/10044/1/93435
DOI: 10.1063/5.0071629
ISSN: 0021-9606
Publisher: American Institute of Physics
Start Page: 074105-1
End Page: 074105-10
Journal / Book Title: Journal of Chemical Physics
Volume: 156
Issue: 7
Copyright Statement: © 2022 Author(s). Published under an exclusive license by AIP Publishing. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Journal of Chemical Physics and may be found at https://aip.scitation.org/doi/10.1063/5.0071629
Sponsor/Funder: Engineering & Physical Science Research Council (E
Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: TUR-000804
EP/L020564/1
Keywords: Density-functional theory
Bayesian statistics
Free-energy functional
Chemical Physics
02 Physical Sciences
03 Chemical Sciences
09 Engineering
Publication Status: Published
Conference Place: USA
Article Number: ARTN 074105
Online Publication Date: 2022-02-16
Appears in Collections:Mathematics
Statistics
Chemical Engineering
Faculty of Natural Sciences
Faculty of Engineering