by Snyder, John C., Rupp, Matthias, Hansen, Katja, Müller, Klaus-Robert and Burke, Kieron
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.
Reference:
Finding Density Functionals with Machine Learning Snyder, John C., Rupp, Matthias, Hansen, Katja, Müller, Klaus-Robert and Burke, Kieron, Phys. Rev. Lett. 108, 253002 (2012). [supplementary information]
Bibtex Entry:
@article{SRHM12,
Pub-num = {137},
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.},
title = {Finding Density Functionals with Machine Learning},
author = {Snyder, John C. and Rupp, Matthias and Hansen, Katja and M\"uller, Klaus-Robert and Burke, Kieron},
journal = {Phys. Rev. Lett.},
volume = {108},
issue = {25},
pages = {253002},
numpages = {5},
year = {2012},
month = {Jun},
doi = {10.1103/PhysRevLett.108.253002},
url = {http://link.aps.org/doi/10.1103/PhysRevLett.108.253002},
publisher = {American Physical Society},
supp-info = {SRHM12_supp},
keywords = {ML}
}