Solving many-electron Schrödinger equation using deep neural networks

Jiequn Han; Linfeng Zhang; Weinan E

doi:10.1016/j.jcp.2019.108929

Solving many-electron Schrödinger equation using deep neural networks

Jiequn Han, Linfeng Zhang, Weinan E

Mathematics

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

137 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	English (US)
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

All Science Journal Classification (ASJC) codes

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

Keywords

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

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10.1016/j.jcp.2019.108929

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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.",

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

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doi = "10.1016/j.jcp.2019.108929",

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T1 - Solving many-electron Schrödinger equation using deep neural networks

AU - Han, Jiequn

AU - Zhang, Linfeng

AU - E, Weinan

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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ER -

Solving many-electron Schrödinger equation using deep neural networks

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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