Dresden 2020 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 24: Complex Fluids and Soft Matter (joint session DY/CPP)
DY 24.8: Talk
Tuesday, March 17, 2020, 11:30–11:45, ZEU 160
Analytical classical density functionals from an equation learning network — •Shang-Chun Lin1, Georg Martius2, and Martin Oettel1 — 1Institut für Angewandte Physik, Eberhard Karls Universität Tübingen, 72076 Tübingen, Germany — 2Max Planck Institute for Intelligent Systems Tübingen, 72076 Tübingen, Germany
We explore the feasibility of using machine learning methods to obtain an analytic form of the classical free energy functional for two model fluids, hard rods and Lennard*Jones, in one dimension. The Equation Learning Network proposed in Ref.[1] is suitably modified to construct free energy densities which are functions of a set of weighted densities and which are built from a small number of basis functions with flexible combination rules. This setup considerably enlarges the functional space used in the machine learning optimization. As a result in Ref [2], we find a good approximation for the exact hard rod functional. For the Lennard--Jones fluid, we let the network learn the full excess free energy functional and the excess free energy functional related to interparticle attractions. Both functionals show a good agreement with simulated density profiles inside and outside the training region. If time allow, we will show the result that forgo the idea gas contribution.
[1]G. Martius and C. H. Lampert, arXiv:1610.02995 (2016).
[2]S.-C. Lin, G. Martius and M. Oettel, arXiv:1910.12752 (2019).