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Why neural functionals suit statistical mechanics

DOI zum Zitieren der Version auf EPub Bayreuth: https://doi.org/10.15495/EPub_UBT_00008152
URN to cite this document: urn:nbn:de:bvb:703-epub-8152-7

Title data

Sammüller, Florian ; Hermann, Sophie ; Schmidt, Matthias:
Why neural functionals suit statistical mechanics.
In: Journal of Physics: Condensed Matter. Vol. 36 (2024) Issue 24 . - 243002.
ISSN 0953-8984
DOI der Verlagsversion: https://doi.org/10.1088/1361-648X/ad326f

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Project information

Project financing: Deutsche Forschungsgemeinschaft

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 Sammüller et al (2023 Proc. Natl Acad. Sci.120 e2312484120) 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 at https://github.com/sfalmo/NeuralDFT-Tutorial.

Further data

Item Type: Article in a journal
Keywords: density functional theory; statistical mechanics; machine learning;
inhomogeneous fluids; fundamental measure theory; neural functional theory;
differential programming
DDC Subjects: 500 Science
500 Science > 530 Physics
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Physics > Chair Theoretical Physics II > Chair Theoretical Physics II - Univ.-Prof. Dr. Matthias Schmidt
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Physics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Physics > Chair Theoretical Physics II
Language: English
Originates at UBT: Yes
URN: urn:nbn:de:bvb:703-epub-8152-7
Date Deposited: 24 Jan 2025 08:06
Last Modified: 24 Jan 2025 08:07
URI: https://epub.uni-bayreuth.de/id/eprint/8152

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