By-passing the Kohn-Sham equations with machine learning

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 these equations. This should yield substantial savings in computer time, allowing either larger systems or longer time-scales to be tackled. Attempts to machine-learn this functional have been limited by the need to find its derivative. The present work overcomes this difficulty, by learning the density-potential map directly. Both the improved accuracy and lower computational cost is demonstrated on DFT calculations of small molecules.