Dresden 2026 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 14: Machine Learning in Dynamics and Statistical Physics II

DY 14.1: Talk

Monday, March 9, 2026, 15:00–15:15, HÜL/S186

Machine-learned classical density functional theory in higher dimensions with convolutional layers — Felix Glitsch, Jens Weimar, and •Martin Oettel — Institut für Angewandte Physik, Universität Tübingen

Through minimization of a grand free energy functional in classical density functional theory (cDFT), inhomogeneous systems in equilibrium can be efficiently computed. For that, the functional of the excess (over ideal gas) free energy is required which is known explicitly only in a few cases. Recent advancements use machine learning for constructing this functional from simulation data, mostly for systems with one-dimensional, planar inhomogeneities. We propose a machine learning model for application in two dimensions [1] akin to density functionals in weighted density forms, as, e.g., in fundamental measure theory. We implement the model with fast convolutional layers only and apply it to a system of hard disks in fully 2D inhomogeneous situations. The model is trained on a combination of smooth and steplike external potentials in the fluid phase. Pair correlation functions from test particle geometry show very satisfactory agreement with simulations although these types of external potentials have not been included in the training. The method should be fully applicable to 3D problems.

[1] F. Glitsch, J. Weimar and M. Oettel, Phys. Rev. E 111, 055305 (2025)

Keywords: classical density functional theory; machine learning; grand canonical simulations