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Finding Density Functionals with Machine Learning
- Issue Date
- 19-Jun-2012
- Publisher
- AMER PHYSICAL SOC
- Keywords
- Functional derivatives; Mean absolute error; Model problems; Noninteracting fermions; Training sets; Electronic structure; Principal component analysis; Learning systems
- Citation
- PHYSICAL REVIEW LETTERS, v.108, no.25
- Indexed
- SCIE
SCOPUS
- Journal Title
- PHYSICAL REVIEW LETTERS
- Volume
- 108
- Number
- 25
- ISSN
- 0031-9007
- 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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