Solving many-electron Schrödinger equation using deep neural networks

Jiequn Han; Linfeng Zhang; Weinan E

doi:https://doi.org/10.1016/j.jcp.2019.108929

Solving many-electron Schrödinger equation using deep neural networks

Jiequn Han, Linfeng Zhang, Weinan E

Mathematics

Princeton University

Research output: Contribution to journal › Article › peer-review

24 Scopus citations

Abstract

We introduce a new family of trial wave-functions based on deep neural networks to solve the many-electron Schrödinger equation. The Pauli exclusion principle is dealt with explicitly to ensure that the trial wave-functions are physical. The optimal trial wave-function is obtained through variational Monte Carlo and the computational cost scales quadratically with the number of electrons. The algorithm does not make use of any prior knowledge such as atomic orbitals. Yet it is able to represent accurately the ground-states of the tested systems, including He, H₂, Be, B, LiH, and a chain of 10 hydrogen atoms. This opens up new possibilities for solving large-scale many-electron Schrödinger equation.

Original language	American English
Article number	108929
Journal	Journal of Computational Physics
Volume	399
DOIs	https://doi.org/10.1016/j.jcp.2019.108929
State	Published - Dec 15 2019

ASJC Scopus subject areas

Numerical Analysis
Modeling and Simulation
Physics and Astronomy (miscellaneous)
Physics and Astronomy(all)
Computer Science Applications
Computational Mathematics
Applied Mathematics

Keywords

Deep neural networks
Schrödinger equation
Trial wave-function
Variational Monte Carlo

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title = "Solving many-electron Schr{\"o}dinger equation using deep neural networks",

abstract = "We introduce a new family of trial wave-functions based on deep neural networks to solve the many-electron Schr{\"o}dinger equation. The Pauli exclusion principle is dealt with explicitly to ensure that the trial wave-functions are physical. The optimal trial wave-function is obtained through variational Monte Carlo and the computational cost scales quadratically with the number of electrons. The algorithm does not make use of any prior knowledge such as atomic orbitals. Yet it is able to represent accurately the ground-states of the tested systems, including He, H2, Be, B, LiH, and a chain of 10 hydrogen atoms. This opens up new possibilities for solving large-scale many-electron Schr{\"o}dinger equation.",

keywords = "Deep neural networks, Schr{\"o}dinger equation, Trial wave-function, Variational Monte Carlo",

author = "Jiequn Han and Linfeng Zhang and Weinan E",

note = "Funding Information: The authors acknowledge M. Motta for helpful discussions. This work is supported in part by Major Program of NNSFC under grant 91130005, ONR grant N00014-13-1-0338 and NSFC grant U1430237. We are grateful for the computing time provided by the High-performance Computing Platform of Peking University and the TIGRESS High Performance Computing Center at Princeton University. Funding Information: The authors acknowledge M. Motta for helpful discussions. This work is supported in part by Major Program of NNSFC under grant 91130005 , ONR grant N00014-13-1-0338 and NSFC grant U1430237 . We are grateful for the computing time provided by the High-performance Computing Platform of Peking University and the TIGRESS High Performance Computing Center at Princeton University. Appendix A Publisher Copyright: {\textcopyright} 2019 Elsevier Inc.",

year = "2019",

month = dec,

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doi = "https://doi.org/10.1016/j.jcp.2019.108929",

language = "American English",

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journal = "Journal of Computational Physics",

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AU - Han, Jiequn

AU - Zhang, Linfeng

AU - E, Weinan

N1 - Funding Information: The authors acknowledge M. Motta for helpful discussions. This work is supported in part by Major Program of NNSFC under grant 91130005, ONR grant N00014-13-1-0338 and NSFC grant U1430237. We are grateful for the computing time provided by the High-performance Computing Platform of Peking University and the TIGRESS High Performance Computing Center at Princeton University. Funding Information: The authors acknowledge M. Motta for helpful discussions. This work is supported in part by Major Program of NNSFC under grant 91130005 , ONR grant N00014-13-1-0338 and NSFC grant U1430237 . We are grateful for the computing time provided by the High-performance Computing Platform of Peking University and the TIGRESS High Performance Computing Center at Princeton University. Appendix A Publisher Copyright: © 2019 Elsevier Inc.

PY - 2019/12/15

Y1 - 2019/12/15

N2 - We introduce a new family of trial wave-functions based on deep neural networks to solve the many-electron Schrödinger equation. The Pauli exclusion principle is dealt with explicitly to ensure that the trial wave-functions are physical. The optimal trial wave-function is obtained through variational Monte Carlo and the computational cost scales quadratically with the number of electrons. The algorithm does not make use of any prior knowledge such as atomic orbitals. Yet it is able to represent accurately the ground-states of the tested systems, including He, H2, Be, B, LiH, and a chain of 10 hydrogen atoms. This opens up new possibilities for solving large-scale many-electron Schrödinger equation.

AB - We introduce a new family of trial wave-functions based on deep neural networks to solve the many-electron Schrödinger equation. The Pauli exclusion principle is dealt with explicitly to ensure that the trial wave-functions are physical. The optimal trial wave-function is obtained through variational Monte Carlo and the computational cost scales quadratically with the number of electrons. The algorithm does not make use of any prior knowledge such as atomic orbitals. Yet it is able to represent accurately the ground-states of the tested systems, including He, H2, Be, B, LiH, and a chain of 10 hydrogen atoms. This opens up new possibilities for solving large-scale many-electron Schrödinger equation.

KW - Deep neural networks

KW - Schrödinger equation

KW - Trial wave-function

KW - Variational Monte Carlo

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JO - Journal of Computational Physics

JF - Journal of Computational Physics

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Solving many-electron Schrödinger equation using deep neural networks

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ASJC Scopus subject areas

Keywords

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