Solving many-electron Schrödinger equation using deep neural networks

Jiequn Han, Linfeng Zhang, Weinan E

Research output: Contribution to journalArticlepeer-review

24 Scopus citations


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 languageAmerican English
Article number108929
JournalJournal of Computational Physics
StatePublished - 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


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


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