Finding Density Functionals with Machine Learning

TL;DR

This paper demonstrates that machine learning can accurately approximate density functionals for non-interacting fermions in 1D, achieving low errors with limited training data and identifying interpolation regions.

Contribution

The study introduces a machine learning approach to density functional approximation, including a predictor for interpolation regions and a method for obtaining accurate self-consistent densities.

Findings

Mean absolute errors below 1 kcal/mol with fewer than 100 training densities

A predictor effectively identifies densities within the interpolation region

Principal component analysis aids in deriving highly accurate self-consistent densities

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.