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Bypassing the Kohn-Sham equations with machine learning

Author

Listed:
  • Felix Brockherde

    (Technische Universität Berlin
    Max-Planck-Institut für Mikrostrukturphysik)

  • Leslie Vogt

    (New York University)

  • Li Li

    (University of California)

  • Mark E. Tuckerman

    (New York University
    New York University
    NYU-ECNU Center for Computational Chemistry at NYU Shanghai)

  • Kieron Burke

    (University of California
    University of California)

  • Klaus-Robert Müller

    (Technische Universität Berlin
    Korea University
    Max-Planck-Institut für Informatik)

Abstract

Last year, at least 30,000 scientific papers used the Kohn–Sham scheme of density functional theory to solve electronic structure problems in a wide variety of scientific fields. Machine learning holds the promise of learning the energy functional via examples, bypassing the need to solve the Kohn–Sham equations. This should yield substantial savings in computer time, allowing larger systems and/or longer time-scales to be tackled, but attempts to machine-learn this functional have been limited by the need to find its derivative. The present work overcomes this difficulty by directly learning the density-potential and energy-density maps for test systems and various molecules. We perform the first molecular dynamics simulation with a machine-learned density functional on malonaldehyde and are able to capture the intramolecular proton transfer process. Learning density models now allows the construction of accurate density functionals for realistic molecular systems.

Suggested Citation

  • Felix Brockherde & Leslie Vogt & Li Li & Mark E. Tuckerman & Kieron Burke & Klaus-Robert Müller, 2017. "Bypassing the Kohn-Sham equations with machine learning," Nature Communications, Nature, vol. 8(1), pages 1-10, December.
    • Handle: RePEc:nat:natcom:v:8:y:2017:i:1:d:10.1038_s41467-017-00839-3
    DOI: 10.1038/s41467-017-00839-3
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    Cited by:

    1. Liu, Yuanbin & Hong, Weixiang & Cao, Bingyang, 2019. "Machine learning for predicting thermodynamic properties of pure fluids and their mixtures," Energy, Elsevier, vol. 188(C).
    2. Yuanming Bai & Leslie Vogt-Maranto & Mark E. Tuckerman & William J. Glover, 2022. "Machine learning the Hohenberg-Kohn map for molecular excited states," Nature Communications, Nature, vol. 13(1), pages 1-10, December.

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