Machine learning of a density functional for anisotropic patchy particles
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866914831528886272 |
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| author | Simon, Alessandro Weimar, Jens Martius, Georg Oettel, Martin |
| author_facet | Simon, Alessandro Weimar, Jens Martius, Georg Oettel, Martin |
| contents | Anisotropic patchy particles have become an archetypical statistical model system for associating fluids. Here we formulate an approach to the Kern-Frenkel model via classical density functional theory to describe the positionally and orientationally resolved equilibrium density distributions in flat wall geometries. The density functional is split into a reference part for the orientationally averaged density and an orientational part in mean-field approximation. To bring the orientational part into a kernel form suitable for machine learning techniques, an expansion into orientational invariants and the proper incorporation of single-particle symmetries is formulated. The mean-field kernel is constructed via machine learning on the basis of hard wall simulation data. Results are compared to the well-known random-phase approximation which strongly underestimates the orientational correlations close to the wall. Successes and shortcomings of the mean-field treatment of the orientational part are highlighted and perspectives are given for attaining a full density functional via machine learning. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2311_04358 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Machine learning of a density functional for anisotropic patchy particles Simon, Alessandro Weimar, Jens Martius, Georg Oettel, Martin Statistical Mechanics Soft Condensed Matter Anisotropic patchy particles have become an archetypical statistical model system for associating fluids. Here we formulate an approach to the Kern-Frenkel model via classical density functional theory to describe the positionally and orientationally resolved equilibrium density distributions in flat wall geometries. The density functional is split into a reference part for the orientationally averaged density and an orientational part in mean-field approximation. To bring the orientational part into a kernel form suitable for machine learning techniques, an expansion into orientational invariants and the proper incorporation of single-particle symmetries is formulated. The mean-field kernel is constructed via machine learning on the basis of hard wall simulation data. Results are compared to the well-known random-phase approximation which strongly underestimates the orientational correlations close to the wall. Successes and shortcomings of the mean-field treatment of the orientational part are highlighted and perspectives are given for attaining a full density functional via machine learning. |
| title | Machine learning of a density functional for anisotropic patchy particles |
| topic | Statistical Mechanics Soft Condensed Matter |
| url | https://arxiv.org/abs/2311.04358 |