Finding Density Functionals with Machine Learning (bibtex)
by John C. Snyder, Matthias Rupp, Katja Hansen, Klaus-Robert Müller, Kieron Burke
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 John C. Snyder, Matthias Rupp, Katja Hansen, Klaus-Robert Müller, Kieron Burke, 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}
	  }
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