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Sammüller, Florian ; Hermann, Sophie ; de las Heras, Daniel ; Schmidt, Matthias:
Neural functional theory for inhomogeneous fluids : Fundamentals and applications.
In: Proceedings of the National Academy of Sciences.
Bd. 120
(2023)
.
- e2312484120.
ISSN 1091-6490
DOI: https://doi.org/10.1073/pnas.2312484120
Abstract
We present a hybrid scheme based on classical density functional theory and machine learning for determining the equilibrium structure and thermodynamics of inhomogeneous fluids. The exact functional map from the density profile to the one-body direct correlation function is represented locally by a deep neural network. We substantiate the general framework for the hard sphere fluid and use grand canonical Monte Carlo simulation data of systems in randomized external environments during training and as reference. Functional calculus is implemented on the basis of the neural network to access higher-order correlation functions via automatic differentiation and the free energy via functional line integration. Thermal Noether sum rules are validated explicitly. We demonstrate the use of the neural functional in the self-consistent calculation of density profiles. The results outperform those from state-of-the-art fundamental measure density functional theory. The low cost of solving an associated Euler–Lagrange equation allows to bridge the gap from the system size of the original training data to macroscopic predictions upon maintaining near-simulation microscopic precision. These results establish the machine learning of functionals as an effective tool in the multiscale description of soft matter.
Weitere Angaben
| Publikationsform: | Artikel in einer Zeitschrift |
|---|---|
| Begutachteter Beitrag: | Ja |
| Institutionen der Universität: | Fakultäten > Fakultät für Mathematik, Physik und Informatik > Physikalisches Institut > Lehrstuhl Theoretische Physik II > Lehrstuhl Theoretische Physik II - Univ.-Prof. Dr. Matthias Schmidt |
| Titel an der UBT entstanden: | Ja |
| Themengebiete aus DDC: | 500 Naturwissenschaften und Mathematik 500 Naturwissenschaften und Mathematik > 530 Physik |
| Eingestellt am: | 27 Mai 2024 11:43 |
| Letzte Änderung: | 27 Mai 2024 11:43 |
| URI: | https://eref.uni-bayreuth.de/id/eprint/89625 |