By-passing the Kohn-Sham equations with machine learning
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.
Keywords
Cite
@article{arxiv.1609.02815,
title = {By-passing the Kohn-Sham equations with machine learning},
author = {Felix Brockherde and Leslie Vogt and Li Li and Mark E. Tuckerman and Kieron Burke and Klaus-Robert Müller},
journal= {arXiv preprint arXiv:1609.02815},
year = {2018}
}