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Machine Learning Kinetic Energy Functional for a One-Dimensional Periodic System |
| Hong-Bin Ren1,2, Lei Wang1,3, and Xi Dai4* |
1Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
2School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
3Songshan Lake Materials Laboratory, Dongguan 523808, China
4Department of Physics, Hong Kong University of Science and Technology, Kowloon 999077, Hong Kong, China
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| Cite this article: |
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Hong-Bin Ren, Lei Wang, and Xi Dai 2021 Chin. Phys. Lett. 38 050701 |
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Abstract Kinetic energy (KE) functional is crucial to speed up density functional theory calculation. However, deriving it accurately through traditional physics reasoning is challenging. We develop a generally applicable KE functional estimator for a one-dimensional (1D) extended system using a machine learning method. Our end-to-end solution combines the dimensionality reduction method with the Gaussian process regression, and simple scaling method to adapt to various 1D lattices. In addition to reaching chemical accuracy in KE calculation, our estimator also performs well on KE functional derivative prediction. Integrating this machine learning KE functional into the current orbital free density functional theory scheme is able to provide us with expected ground state electron density.
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Received: 26 January 2021
Published: 02 May 2021
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| PACS: |
71.15.Mb
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(Density functional theory, local density approximation, gradient and other corrections)
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07.05.Mh
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(Neural networks, fuzzy logic, artificial intelligence)
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02.50.Ey
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(Stochastic processes)
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| Fund: Supported by the Hong Kong Research Grants Council (Project No. GRF16300918), the National Key R&D Program of China (Grant Nos. 2016YFA0300603 and 2016YFA0302400), and the National Natural Science Foundation of China (Grant No. 11774398). |
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| [1] | Kohn W and Sham L J 1965 Phys. Rev. 140 A1133 |
| [2] | Hafner J, Wolverton C, and Ceder G 2006 MRS Bull. 31 659 |
| [3] | Jones R O 2015 Rev. Mod. Phys. 87 897 |
| [4] | Wu Y, Schuster M, Chen Z, Le Q V, and Norouzi M 2016 arXiv:1609.08144 [cs.CL] |
| [5] | Hinton G, Deng L, Yu D, Dahl G, and Mohamed A R 2012 IEEE Signal Process. Mag. 29 29 |
| [6] | Krizhevsky A, Sutskever I, and Hinton G E 2012 Imagenet Classification with Deep Convolutional Neural Networks in Advances in Neural Information Processing Systems ed Pereira F, Burges C J C, Bottou L and Weinberger K Q (Curran Associates, Inc.) vol 25 pp 1097–1105 |
| [7] | Behler J and Parrinello M 2007 Phys. Rev. Lett. 98 146401 |
| [8] | Bartók A P, Payne M C, Kondor R, and Csányi G 2010 Phys. Rev. Lett. 104 136403 |
| [9] | Rupp M, Tkatchenko A, Müller K R, and Von Lilienfeld O A 2012 Phys. Rev. Lett. 108 058301 |
| [10] | Zhang L, Han J, Wang H, Car R, and Weinan E 2018 Phys. Rev. Lett. 120 143001 |
| [11] | Ramakrishnan R, Dral P O, Rupp M, and von Lilienfeld O A 2014 Sci. Data 1 140022 |
| [12] | Gilmer J, Schoenholz S S, Riley P F, Vinyals O, and Dahl G E 2017 Proceedings of the 34th International Conference on Machine Learning (ICML'17) vol 70 pp 1263–1272 |
| [13] | Chen G, Chen P, Hsieh C Y, Lee C K, and Liao B 2019 arXiv:1906.09427 [cs.LG] |
| [14] | Zhuang L, Ye Q, Pan D, and Li X Z 2020 Chin. Phys. Lett. 37 043101 |
| [15] | Yao T S, Tang C Y, Yang M, Zhu K J, and Yan D Y 2019 Chin. Phys. Lett. 36 068101 |
| [16] | Tang Q, Yang J H, Liu Z P, and Gong X G 2020 Chin. Phys. Lett. 37 096802 |
| [17] | Snyder J C, Rupp M, Hansen K, Müller K R, and Burke K 2012 Phys. Rev. Lett. 108 253002 |
| [18] | Lignères V L and Carter E A 2005 Handbook of Materials Modeling (Berlin: Springer) p 137 |
| [19] | Witt W C, Beatriz G, Dieterich J M, and Carter E A 2018 J. Mater. Res. 33 777 |
| [20] | Bengio Y, Delalleau O, and Le R N 2005 Département d'Informatique et Recherche Opérationnelle, Université de Montréal, Canada Tech. Rep. 1258 |
| [21] | Schölkopf B, Herbrich R, and Smola A J 2001 International Conference on Computational Learning Theory (COLT 2001) in Lecture Notes in Computer Science (Berlin: Springer) vol 2111 pp 416–426 |
| [22] | Alvarez M A, Rosasco L, and Lawrence N D 2011 arXiv:1106.6251 [stat.ML] |
| [23] | MacKay D J 1998 NATO ASI Ser. F: Comput. Syst. Sci. 168 133 |
| [24] | Calandra R, Peters J, Rasmussen C E, and Deisenroth M P 2016 2016 International Joint Conference on Neural Networks (IJCNN) (24-29 July 2016, Vancouver, BC, Canada) pp 3338–3345 |
| [25] | Stein M L 2012 Interpolation of Spatial Data: Some Theory for Kriging (Berlin: Springer) |
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