Exact expressions for structure selection in cluster expansions
Name
Mueller-2010-Exact expressions fo.pdf
Size
393.58 KB
Format
Adobe PDF
Checksum (MD5)
6ebce5fdfafa1fa19002470013d16e7f
Author(s)
Mueller, Timothy K.
Ceder, Gerbrand
Date Issued
August 2010
Journal
Physical Review B
Publisher
American Physical Society
Citation
Mueller, Tim and Gerbrand Ceder. "Exact expressions for structure selection in cluster expansions." Phys. Rev. B 82, 184107 (2010) © 2010 The American Physical Society.
Version
Final published version
Abstract
The cluster expansion has proven to be a valuable tool in materials science to predict properties of configurationally ordered and disordered structures but the generation of cluster expansions can be computationally expensive. In recent years there have been efforts to make the generation of cluster expansions more efficient by selecting training structures in a way that minimizes approximate expressions for the variance of the predicted property values. We demonstrate that in many cases, these approximations are not necessary and exact expressions for the variance of the predicted property values may be derived. To illustrate this result, we present examples based on common applications of the cluster expansion such as bulk binary alloys. In addition we extend these structure selection techniques to Bayesian cluster expansions. These results should enable researchers to better analyze the quality of existing training sets and to select training structures that yield cluster expansions with lower prediction error.
MIT Department
Massachusetts Institute of Technology. Department of Materials Science and Engineering
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1103/PhysRevB.82.184107
