By-passing the Kohn-Sham equations with machine learning
This addresses the high computational cost for researchers in fields like materials science and biochemistry, though it is incremental as it builds on prior attempts to machine-learn the kinetic energy functional.
The paper tackled the computational bottleneck of solving Kohn-Sham equations in density functional theory by using machine learning to directly learn density-potential and energy-density maps, demonstrating improved accuracy and lower computational cost in reproducing DFT energies for molecular geometries.
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.