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Development of an exchange–correlation functional with uncertainty quantification capabilities for density functional theory
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Aldegunde, Manuel, Kermode, James R. and Zabaras , Nicholas (2016) Development of an exchange–correlation functional with uncertainty quantification capabilities for density functional theory. Journal of Computational Physics, 311 . pp. 173-195. doi:10.1016/j.jcp.2016.01.034 ISSN 0021-9991.
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Official URL: http://dx.doi.org/10.1016/j.jcp.2016.01.034
Abstract
This paper presents the development of a new exchange–correlation functional from the point of view of machine learning. Using atomization energies of solids and small molecules, we train a linear model for the exchange enhancement factor using a Bayesian approach which allows for the quantification of uncertainties in the predictions. A relevance vector machine is used to automatically select the most relevant terms of the model. We then test this model on atomization energies and also on bulk properties. The average model provides a mean absolute error of only 0.116 eV for the test points of the G2/97 set but a larger 0.314 eV for the test solids. In terms of bulk properties, the prediction for transition metals and monovalent semiconductors has a very low test error. However, as expected, predictions for types of materials not represented in the training set such as ionic solids show much larger errors.
Item Type: | Journal Article | ||||||||||
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Subjects: | Q Science > QD Chemistry | ||||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Engineering > Engineering | ||||||||||
Library of Congress Subject Headings (LCSH): | Density functionals, Mathematical physics, Quantum theory, Uncertainty (Information theory) -- Mathematical models, Bayesian statistical decision theory | ||||||||||
Journal or Publication Title: | Journal of Computational Physics | ||||||||||
Publisher: | Academic Press Inc. Elsevier Science | ||||||||||
ISSN: | 0021-9991 | ||||||||||
Official Date: | 15 April 2016 | ||||||||||
Dates: |
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Volume: | 311 | ||||||||||
Page Range: | pp. 173-195 | ||||||||||
DOI: | 10.1016/j.jcp.2016.01.034 | ||||||||||
Status: | Peer Reviewed | ||||||||||
Publication Status: | Published | ||||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||||
Date of first compliant deposit: | 19 February 2016 | ||||||||||
Date of first compliant Open Access: | 1 February 2017 | ||||||||||
Funder: | Engineering and Physical Sciences Research Council (EPSRC), Seventh Framework Programme (European Commission) (FP7) | ||||||||||
Grant number: | EP/L027682/1, 291763 |
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