By-passing the Kohn-Sham equations with machine learning

2016/09/30 by Felix Brockherde, Leslie Vogt, Li Li +3 · 5 citations
Physics and Astronomy · Computer Science · Mathematics · #physics.comp-ph #cs.LG #physics.chem-ph #stat.ML

paper · pdf · doi:10.1038/s41467-017-00839-3

arxiv created 2017/06/15 · arxiv updated 2018/02/07

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, ranging from materials science to biochemistry to astrophysics. Machine learning holds the promise of learning the kinetic energy functional via examples, by-passing the need to solve the Kohn-Sham equations. This should yield substantial savings in computer time, allowing either larger systems 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. Both improved accuracy and lower computational cost with this method are demonstrated by reproducing DFT energies for a range of molecular geometries generated during molecular dynamics simulations. Moreover, the methodology could be applied directly to quantum chemical calculations, allowing construction of density functionals of quantum-chemical accuracy.

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