Berlin 2024 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 5: Machine Learning in Dynamics and Statistical Physics I
DY 5.6: Vortrag
Montag, 18. März 2024, 10:45–11:00, BH-N 243
Machine learning of a density functional for anisotropic patchy particles — •Alessandro Simon1,2, Martin Oettel1, and Georg Martius2 — 1University of Tübingen, Tübingen, Germany — 2Max Planck Institute for Intelligent Systems, Tübingen, Germany
Anisotropic patchy particles have become an archetypical statistical model system for associating fluids. Here we formulate an approach to the Kern-Frenkel model via classical density functional theory to describe the positionally and orientationally resolved equilibrium density distributions in flat wall geometries. After investigating the orientational structure of the fluid close to the wall, we bring the anisotropic part of the free energy into a kernel-form suitable for machine learning, through an expansion into orientational invariants and the proper incorporation of the tetrahedral single-particle symmetries. The mean-field kernel is constructed via machine learning on the basis of hard wall simulation data and a robust and numerically stable method that is able to condition neural networks on fixed points of their output. Results are compared to other well-known mean-field approximations, which strongly underestimate orientational correlation. Finally, we propose more general machine-learning methods that are able to go beyond the mean-field approximation.
Keywords: classical fluids; density functional theory; machine learning; invariance; orientational