Exact expressions for structure selection in cluster expansions
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 cluste...
| Main Authors: | , |
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| 其他作者: | |
| 格式: | 文件 |
| 语言: | en_US |
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American Physical Society
2011
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| 在线阅读: | http://hdl.handle.net/1721.1/63804 |
| _version_ | 1826216609980612608 |
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| author | Mueller, Timothy K. Ceder, Gerbrand |
| author2 | Massachusetts Institute of Technology. Department of Materials Science and Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Materials Science and Engineering Mueller, Timothy K. Ceder, Gerbrand |
| author_sort | Mueller, Timothy K. |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T16:50:11Z |
| format | Article |
| id | mit-1721.1/63804 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T16:50:11Z |
| publishDate | 2011 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/638042022-09-29T21:51:24Z Exact expressions for structure selection in cluster expansions Mueller, Timothy K. Ceder, Gerbrand Massachusetts Institute of Technology. Department of Materials Science and Engineering Ceder, Gerbrand Mueller, Timothy K. Ceder, Gerbrand 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. United States. Dept. of Energy (Contract No. DE-FG02-96ER45571) 2011-06-09T17:18:47Z 2011-06-09T17:18:47Z 2010-08 2010-11 Article http://purl.org/eprint/type/JournalArticle 1098-0121 1550-235X http://hdl.handle.net/1721.1/63804 Mueller, Tim and Gerbrand Ceder. "Exact expressions for structure selection in cluster expansions." Phys. Rev. B 82, 184107 (2010) © 2010 The American Physical Society. en_US http://dx.doi.org/10.1103/PhysRevB.82.184107 Physical Review B 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. application/pdf American Physical Society APS |
| spellingShingle | Mueller, Timothy K. Ceder, Gerbrand Exact expressions for structure selection in cluster expansions |
| title | Exact expressions for structure selection in cluster expansions |
| title_full | Exact expressions for structure selection in cluster expansions |
| title_fullStr | Exact expressions for structure selection in cluster expansions |
| title_full_unstemmed | Exact expressions for structure selection in cluster expansions |
| title_short | Exact expressions for structure selection in cluster expansions |
| title_sort | exact expressions for structure selection in cluster expansions |
| url | http://hdl.handle.net/1721.1/63804 |
| work_keys_str_mv | AT muellertimothyk exactexpressionsforstructureselectioninclusterexpansions AT cedergerbrand exactexpressionsforstructureselectioninclusterexpansions |