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Analytical classical density functionals from an equation learning network
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DOI：10.1063/1.5135919.png)
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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 by Martius and Lampert [e-print arXiv:1610.02995 (2016)] 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 compared to the previous work [S.-C. Lin and M. Oettel, SciPost Phys. 6, 025 (2019)] where the functional is limited to a simple polynomial form. As a result, we find a good approximation for the exact hard rod functional and its direct correlation function. For the Lennard-Jones fluid, we let the network learn (i) the full excess free energy functional and (ii) the excess free energy functional related to interparticle attractions. Both functionals show a good agreement with simulated density profiles for thermodynamic parameters inside and outside the training region.
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FLUID
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IF:
3.1
论文数:
7.2W
被引数:
23.2W
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Proceedings of the 18th ACM SIGKDD international conference on Knowledge discovery and data mining
Proceedings of the 18th ACM SIGKDD international conference on Knowledge discovery and data miningIF0
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