Finding Density Functionals with Machine Learning

Abstract

Machine learning is used to approximate density functionals. For the model problem of the kinetic energy of non-interacting 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. Challenges for application of our method to real electronic structure problems are discussed.

4 pages, 4 figures, 1 table. The Supplemental Material is included at the end of the manuscript (2 pages, 3 tables)