Machine learning-guided construction of an analytic kinetic energy functional for orbital free density functional theory
Machine learning (ML) of kinetic energy functionals (KEF) for orbital-free density functional theory (DFT) holds the promise of addressing an important bottleneck in large-scale ab initio materials modeling where sufficiently accurate analytic KEFs are lacking. However, ML models are not as easily h...
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IOP Publishing
2025-01-01
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| Series: | Machine Learning: Science and Technology |
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| Online Access: | https://doi.org/10.1088/2632-2153/ade7ca |
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| author | Sergei Manzhos Johann Lüder Pavlo Golub Manabu Ihara |
| author_facet | Sergei Manzhos Johann Lüder Pavlo Golub Manabu Ihara |
| author_sort | Sergei Manzhos |
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| description | Machine learning (ML) of kinetic energy functionals (KEF) for orbital-free density functional theory (DFT) holds the promise of addressing an important bottleneck in large-scale ab initio materials modeling where sufficiently accurate analytic KEFs are lacking. However, ML models are not as easily handled as analytic expressions; they need to be provided in the form of algorithms and associated data. Here, we bridge the two approaches and construct an analytic expression for a KEF guided by interpretative ML of crystal cell-averaged kinetic energy densities ( ${\bar{\tau}}$ ) of several hundred materials. A previously published dataset including multiple phases of 433 unary, binary, and ternary compounds containing Li, Al, Mg, Si, As, Ga, Sb, Na, Sn, P, and In was used for training, including data at the equilibrium geometry as well as strained structures. A hybrid Gaussian process regression—neural network method was used to understand the type of functional dependence of $\overline\tau$ on the features which contained cell-averaged terms of the 4th order gradient expansion and the product of the electron density and Kohn–Sham (KS) effective potential. Based on this analysis, an analytic model is constructed that can reproduce KS DFT energy–volume curves with sufficient accuracy (pronounced minima that are sufficiently close to the minima of the Kohn–Sham DFT-based curves and with sufficiently close curvatures) to enable structure optimizations and elastic response calculations. |
| format | Article |
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| issn | 2632-2153 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | IOP Publishing |
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| series | Machine Learning: Science and Technology |
| spelling | doaj-art-0c64b1a6f84d4da2bcc4f1919cfe40102025-07-03T08:59:58ZengIOP PublishingMachine Learning: Science and Technology2632-21532025-01-016303500210.1088/2632-2153/ade7caMachine learning-guided construction of an analytic kinetic energy functional for orbital free density functional theorySergei Manzhos0https://orcid.org/0000-0001-8172-7903Johann Lüder1https://orcid.org/0000-0001-6603-8376Pavlo Golub2Manabu Ihara3School of Materials and Chemical Technology, Institute of Science Tokyo , Ookayama 2-12-1, Meguro-ku, Tokyo 152-8552, JapanDepartment of Materials and Optoelectronic Science, National Sun Yat-sen University , 80424, No. 70, Lien-Hai Road, Kaohsiung, TaiwanDepartment of Theoretical Chemistry, J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic , 3 Dolejškova 2155, Libeň, 182 00 Praha 8, Czech RepublicSchool of Materials and Chemical Technology, Institute of Science Tokyo , Ookayama 2-12-1, Meguro-ku, Tokyo 152-8552, JapanMachine learning (ML) of kinetic energy functionals (KEF) for orbital-free density functional theory (DFT) holds the promise of addressing an important bottleneck in large-scale ab initio materials modeling where sufficiently accurate analytic KEFs are lacking. However, ML models are not as easily handled as analytic expressions; they need to be provided in the form of algorithms and associated data. Here, we bridge the two approaches and construct an analytic expression for a KEF guided by interpretative ML of crystal cell-averaged kinetic energy densities ( ${\bar{\tau}}$ ) of several hundred materials. A previously published dataset including multiple phases of 433 unary, binary, and ternary compounds containing Li, Al, Mg, Si, As, Ga, Sb, Na, Sn, P, and In was used for training, including data at the equilibrium geometry as well as strained structures. A hybrid Gaussian process regression—neural network method was used to understand the type of functional dependence of $\overline\tau$ on the features which contained cell-averaged terms of the 4th order gradient expansion and the product of the electron density and Kohn–Sham (KS) effective potential. Based on this analysis, an analytic model is constructed that can reproduce KS DFT energy–volume curves with sufficient accuracy (pronounced minima that are sufficiently close to the minima of the Kohn–Sham DFT-based curves and with sufficiently close curvatures) to enable structure optimizations and elastic response calculations.https://doi.org/10.1088/2632-2153/ade7caorbital-free DFTkinetic energy functionalGaussian process regressionadditive kernel |
| spellingShingle | Sergei Manzhos Johann Lüder Pavlo Golub Manabu Ihara Machine learning-guided construction of an analytic kinetic energy functional for orbital free density functional theory Machine Learning: Science and Technology orbital-free DFT kinetic energy functional Gaussian process regression additive kernel |
| title | Machine learning-guided construction of an analytic kinetic energy functional for orbital free density functional theory |
| title_full | Machine learning-guided construction of an analytic kinetic energy functional for orbital free density functional theory |
| title_fullStr | Machine learning-guided construction of an analytic kinetic energy functional for orbital free density functional theory |
| title_full_unstemmed | Machine learning-guided construction of an analytic kinetic energy functional for orbital free density functional theory |
| title_short | Machine learning-guided construction of an analytic kinetic energy functional for orbital free density functional theory |
| title_sort | machine learning guided construction of an analytic kinetic energy functional for orbital free density functional theory |
| topic | orbital-free DFT kinetic energy functional Gaussian process regression additive kernel |
| url | https://doi.org/10.1088/2632-2153/ade7ca |
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