TY - JOUR

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

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

UR - http://www.scopus.com/inward/record.url?scp=85072698605&partnerID=8YFLogxK

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U2 - 10.1016/j.jcp.2019.108929

DO - 10.1016/j.jcp.2019.108929

M3 - Article

AN - SCOPUS:85072698605

VL - 399

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

M1 - 108929

ER -