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Phys Rev Lett. 2012 Jun 22;108(25):253002. Epub 2012 Jun 19.

Finding density functionals with machine learning.

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1
Departments of Chemistry and of Physics, University of California, Irvine, California 92697, USA.

Abstract

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.

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