Bulletin of the American Physical Society
APS March Meeting 2024
Monday–Friday, March 4–8, 2024; Minneapolis & Virtual
Session OD01: V: On-Demand Presentations - Available throughout March Meeting
6:00 AM,
Sunday, March 3, 2024
Abstract: OD01.00011 : Data-Driven Solution of the Inverse Problem of Classical Statistical Mechanics
Presenter:
Peter Yatsyshin
(The Alan Turing Institute)
Authors:
Peter Yatsyshin
(The Alan Turing Institute)
Serafim Kalliadasis
(Imperial College London)
Usually DFT approximations are interpretable and amenable to computation. This explains the popularity of DFTs across fundamental applications of statistical mechanics. However therein lies the principal challenge of using DFTs in engineering: one must know (or postulate) the density functional of the system under consideration. This is highly challenging in realistic scenarios encountered in, e.g., biology, nanotechnology and chemical engineering. Our talk aims to address this challenge.
We pose the inverse problem of statistical mechanics: given particle data, characterise the free energy functional of the system. We then solve it using Bayesian reasoning. In the process, we develop a data-efficient learning algorithm that automates the construction of approximate free-energy functionals from small amounts of simulation data. On output the user gets a probability distribution over DFTs with full uncertainty quantification, allowing one to scale the description to system sizes far beyond the simulation capabilities. Our approach leverages modern computational capabilities in a physics-constrained framework to learn the free energy in a data-driven automated fashion. We validate our algorithm by consideing classical particle systems with excluded volume interactions. Such systems are ubiquitous in nature, while being highly challenging in terms of free energy modeling. We demonstrate that with appropriate particle data we can learn both the canonical and grand-canonical free-energy representations of such systems. Extensions to more complex and higher-dimensional systems are conceptually straightforward.
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