Sammüller F, Hermann S, Schmidt M. Why neural functionals suit statistical mechanics.
J Phys Condens Matter 2024;
36:243002. [PMID:
38467072 DOI:
10.1088/1361-648x/ad326f]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/29/2023] [Accepted: 03/11/2024] [Indexed: 03/13/2024]
Abstract
We describe recent progress in the statistical mechanical description of many-body systems via machine learning combined with concepts from density functional theory and many-body simulations. We argue that the neural functional theory by Sammülleret al(2023Proc. Natl Acad. Sci.120e2312484120) gives a functional representation of direct correlations and of thermodynamics that allows for thorough quality control and consistency checking of the involved methods of artificial intelligence. Addressing a prototypical system we here present a pedagogical application to hard core particle in one spatial dimension, where Percus' exact solution for the free energy functional provides an unambiguous reference. A corresponding standalone numerical tutorial that demonstrates the neural functional concepts together with the underlying fundamentals of Monte Carlo simulations, classical density functional theory, machine learning, and differential programming is available online athttps://github.com/sfalmo/NeuralDFT-Tutorial.
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