Abstract

Classical density functional theory and power functional theory provide formally exact frameworks for the description of many-body systems in and out of equilibrium. In the talk I show how machine learning can be applied effectively in these theories in order to characterize inhomogeneous fluids. Neural networks which are trained with simulation data facilitate precise and flexible representations of the central functional maps. These neural functionals can be utilized straightforwardly for predictions which supersede analytic treatments in accuracy. Additionally, they enable access to more fundamental related quantities, which forms the basis of a stand-alone theoretical framework. Successful applications include multiscale problems, such as colloidal sedimentation-diffusion equilibrium under gravity, and the inverse design of nonequilibrium flow.

• F. Sammüller, S. Hermann, and M. Schmidt, arXiv:2312.04681
• F. Sammüller, S. Hermann, D. de las Heras, and M. Schmidt, Proc. Nat. Acad. Sci. 120, e2312484120 (2023), doi:10.1073/pnas.2312484120
• D. de las Heras, T. Zimmermann, F. Sammüller, S. Hermann, and M. Schmidt, J. Phys.: Condens. Matter 35, 271501 (2023), doi:10.1088/1361-648X/accb33