Bypassing the Kohn-Sham equations with machine learning

Felix Brockherde, Leslie Vogt, Li Li, Mark E. Tuckerman (), Kieron Burke () and Klaus-Robert Müller ()
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Felix Brockherde: Technische Universität Berlin
Leslie Vogt: New York University
Li Li: University of California
Mark E. Tuckerman: New York University
Kieron Burke: University of California
Klaus-Robert Müller: Technische Universität Berlin

Nature Communications, 2017, vol. 8, issue 1, 1-10

Abstract: 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.

Date: 2017
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DOI: 10.1038/s41467-017-00839-3

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