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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.08143 |
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| _version_ | 1866929624522424320 |
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| author | Mitchell, Michael A. J. Ferrandis, Teresa Del Aguila Sanvito, Stefano |
| author_facet | Mitchell, Michael A. J. Ferrandis, Teresa Del Aguila Sanvito, Stefano |
| contents | Orbital-free density functional theory promises to deliver linear-scaling electronic structure calculations. This requires the knowledge of the non-interacting kinetic-energy density functional (KEDF), which should be accurate and must admit accurate functional derivatives, so that a minimization procedure can be designed. In this work, symbolic regression is explored as an alternative means to machine-learn the KEDF, which results into analytical expressions, whose functional derivatives are easy to compute. The so-determined semi-local functional forms are investigated as a function of the electron number, and we are able to track the transition from the von Weizsäcker functional, exact for the one-electron case, to the Thomas-Fermi functional, exact in the homogeneous electron gas limit. A number of separate searches are performed, ranging from totally unconstrained to constrained in the form of an enhancement factor. This work highlights the complexity in constructing semi-local approximations of the KEDF and the potential of symbolic regression to advance the search. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_08143 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | 1D Kinetic Energy Density Functionals learned with Symbolic Regression Mitchell, Michael A. J. Ferrandis, Teresa Del Aguila Sanvito, Stefano Materials Science Orbital-free density functional theory promises to deliver linear-scaling electronic structure calculations. This requires the knowledge of the non-interacting kinetic-energy density functional (KEDF), which should be accurate and must admit accurate functional derivatives, so that a minimization procedure can be designed. In this work, symbolic regression is explored as an alternative means to machine-learn the KEDF, which results into analytical expressions, whose functional derivatives are easy to compute. The so-determined semi-local functional forms are investigated as a function of the electron number, and we are able to track the transition from the von Weizsäcker functional, exact for the one-electron case, to the Thomas-Fermi functional, exact in the homogeneous electron gas limit. A number of separate searches are performed, ranging from totally unconstrained to constrained in the form of an enhancement factor. This work highlights the complexity in constructing semi-local approximations of the KEDF and the potential of symbolic regression to advance the search. |
| title | 1D Kinetic Energy Density Functionals learned with Symbolic Regression |
| topic | Materials Science |
| url | https://arxiv.org/abs/2412.08143 |