Accurate approximations to density functionals have recently been obtained via machine learning (ML). By applying ML to a simple function of one variable without any random sampling, we extract the qualitative dependence of errors on hyperparameters. We find universal features of the behavior in extreme limits, including both very small and very large length scales, and the noise-free limit. We show how such features arise in ML models of density functionals.
Bibliographical notePublisher Copyright:
© 2015 Wiley Periodicals, Inc.
- density functional theory
- extreme behaviors
- hyperparameters optimization
- machine learning
- noise-free curve
ASJC Scopus subject areas
- Atomic and Molecular Physics, and Optics
- Condensed Matter Physics
- Physical and Theoretical Chemistry