## Title data

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.
Vol. 120
(2023)
.
- e2312484120.

ISSN 1091-6490

DOI: https://doi.org/10.1073/pnas.2312484120

## Abstract in another language

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.

## Further data

Item Type: | Article in a journal |
---|---|

Refereed: | Yes |

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 |

Result of work at the UBT: | Yes |

DDC Subjects: | 500 Science 500 Science > 530 Physics |

Date Deposited: | 27 May 2024 11:43 |

Last Modified: | 27 May 2024 11:43 |

URI: | https://eref.uni-bayreuth.de/id/eprint/89625 |