Dresden 2026 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 41: Poster: Nonlinear Dynamics, Granular Matter, and Machine Learning

DY 41.14: Poster

Wednesday, March 11, 2026, 15:00–18:00, P5

Machine Learning of a Classical Density Functional for 2D Hard Rods — •Paul Bitzer, Jens Weimar, and Martin Oettel — Eberhard Karls University of Tübingen, Tübingen, Germany

Obtaining phase diagrams and density distributions via Grand canonical Monte Carlo simulations (GCMC) for classical fluids still requires substantial computational resources. Here, classical density functional theory (cDFT) is more efficient if the excess functional for the free energy is known. Recently, machine learning (ML) methods have become popular to learn such functionals (which are broadly applicable) from a limited amount of training data obtained in random, inhomogeneous external potentials [1]. We discuss an extension of an ML scheme to lattice fluids and apply it to the case of hard rods in two dimensions (2D). This model shows demixing between majority phases of vertically resp. horizontally oriented rods. This is typical of demixing in a binary, continumm fluid whose phase diagram has been learned recently in [2] employing only training data inhomogeneous in 1D. The use of explicit 2D training data allows applications to more general inhomogeneous situations [3].

[1] A. Simon and M. Oettel, Machine learning approaches to classical density functional theory (review), arXiv:2406.07345

[2] S. Robitschko et al, J. Chem. Phys. 163, 161101 (2025)

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

Keywords: classical density functional theory; machine learning; grand canonical Monte Carlo simulations; 2D Hard Rods