Finding density functionals with machine learning

Phys Rev Lett. 2012 Jun 22;108(25):253002. doi: 10.1103/PhysRevLett.108.253002. Epub 2012 Jun 19.


Machine learning is used to approximate density functionals. For the model problem of the kinetic energy of noninteracting fermions in 1D, mean absolute errors below 1 kcal/mol on test densities similar to the training set are reached with fewer than 100 training densities. A predictor identifies if a test density is within the interpolation region. Via principal component analysis, a projected functional derivative finds highly accurate self-consistent densities. The challenges for application of our method to real electronic structure problems are discussed.