BPCPPDYSOE21 – scientific programme
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CPP: Fachverband Chemische Physik und Polymerphysik
CPP 20: Complex Fluids and Soft Matter 2 (joint session DY/CPP)
CPP 20.4: Talk
Wednesday, March 24, 2021, 12:00–12:20, DYa
Analytical classical density functionals from an equation learning network — •ShangChun Lin1, Georg Martius2, and Martin Oettel1 — 1Institut für Angewandte Physik, Universität Tübingen, Tübingen, Germany — 2Max Planck Institute for Intelligent Systems, 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 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.
[1]G. Martius and C. H. Lampert, arXiv:1610.02995 (2016).
[2]S.-C. Lin, G. Martius and M. Oettel, JCP 152.2 (2020): 021102.