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University of Bayreuth, Press Release No. 171 /2023 - 13 December 2023 

Breakthrough for describing soft matter through AI at the University of Bayreuth

Scientists from Bayreuth have developed a new method for studying liquid and soft matter using artificial intelligence. In a study now published in the renowned journal "Proceedings of the National Academy of Sciences of the United States of America" (PNAS), they open up a new chapter in density functional theory with their "neural functional theory".

We live in a highly technologised world where basic research is the engine of innovation, in a dense and complex web of interrelationships and interdependencies. The published research provides new methods that can have a great influence on widespread simulation techniques, so that complex substances can be investigated on computers more quickly, more precisely and more deeply. In the future, this could have an influence on product and process design. The fact that the structure of liquids can be excellently represented by the newly formulated neural mathematical relationships is a major breakthrough that opens up a range of possibilities for gaining deep physical insights.


The illustration shows the workflow inherent in the neural functional theory, starting with data acquisition via sampling in particle-based computer simulations. A neural network is trained to represent direct correlations that are intrinsic to the physical system at hand. The theory can then be freely applied to real physical problems, more quickly and in greater depth than what was possible before.

"In the study, we demonstrate how artificial intelligence can be used to carry out fundamental theoretical physics that addresses the behaviour of fluids and other complex soft matter systems," says Prof. Dr. Matthias Schmidt, Chair of Theoretical Physics II at the University of Bayreuth, and explains: "We have developed an advanced scientific method to study matter at the atomic and (macro)molecular level, combining machine learning and mathematical methods to calculate complex physical properties."

The Bayreuth researchers present a hybrid scheme based on classical density functional theory and machine learning to determine the equilibrium structure and thermodynamics of fluids under a variety of influences. Schmidt reports: "We demonstrate the use of the neural functional in the self-consistent computation of density profiles. The quality of the results exceeds the state of the art of fundamental-measure density functional theory. The results establish machine learning of functionals as an efficient tool for the multiscale description of soft matter." Thus, fundamental insights into the structure of matter are gained. The type of matter can be mundane, but it can also be the basis of technological processes and commercial products. "This powerful combination of essentially simple basic techniques has opened a new chapter in density functional theory," says Schmidt, "because networks trained by simulation data are more accurate than the currently best theoretical approximations designed 'by hand', i.e. with paper and pencil."

The team from left:  Prof. Dr. Matthias Schmidt, Sabrina Süss, Florian Sammüller, M.Sc., Prof. Dr. Daniel de las Heras, Dr. Sophie Hermann.

Schmidt emphasises: "In addition to the significance for the particular field of statistical mechanics of soft matter, I think our method also raises fundamental questions about the human self-understanding of our intellectual activity. For myself, our study gives considerable hope for developments where artificial intelligence, rather than replacing us, expands us in a way that I find very surprising."

The study was funded as part of a DFG project.

The researchers at the University of Bayreuth also provide broadly accessible tutorial material to accompany the PNAS publication. This includes a further introductory article ("Why neural functionals suit statistical mechanics" by Florian Sammüller, Sophie Hermann, and Matthias Schmidt) as well as programming code available online, which interested people can try out for themselves and also work with.

Neural functional theory for inhomogeneous fluids: Fundamentals and applications
Florian Sammüller, Sophie Hermann, Daniel de las Heras, and Matthias Schmidt, Proc. Nat. Acad. Sci. 120, e2312484120 (2023).
DOI: https://doi.org/10.1073/pnas.2312484120

Why neural functionals suit statistical mechanics
Florian Sammüller, Sophie Hermann, and Matthias Schmidt, arXiv:2312.04681
DOI: https://doi.org/10.48550/arXiv.2312.04681

Neural functional theory for inhomogeneous fluids - Tutorial
Florian SammüllerFundort: https://github.com/sfalmo/NeuralDFT-Tutorial

Prof. Dr. Matthias Schmidt

Prof. Dr. Matthias Schmidt

Theoretical Physics II
University of Bayreuth

Portraitbild von Anja Maria Meister

Anja-Maria Meister

PR Spokesperson University of Bayreuth

Phone: +49 (0) 921  55 - 5300
E-mail: anja.meister@uni-bayreuth.de