Bayesian approach to cluster expansions
Cluster expansions have proven to be a valuable tool in alloy theory and other problems in materials science but the generation of cluster expansions can be a computationally expensive and time-consuming process. We present a Bayesian framework for developing cluster expansions that explicitly incor...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
American Physical Society
2010
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| Online Access: | http://hdl.handle.net/1721.1/51374 |
| _version_ | 1826216355365388288 |
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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 | Cluster expansions have proven to be a valuable tool in alloy theory and other problems in materials science but the generation of cluster expansions can be a computationally expensive and time-consuming process. We present a Bayesian framework for developing cluster expansions that explicitly incorporates physical insight into the fitting procedure. We demonstrate how existing methods fit within this framework and use the framework to develop methods that significantly improve the predictive power of cluster expansions for a given training set size. The key to the methods is to apply physical insight and cross validation to develop physically meaningful prior probability distributions for the cluster expansion coefficients. We use the Bayesian approach to develop an efficient method for generating cluster expansions for low-symmetry systems such as surfaces and nanoparticles. |
| first_indexed | 2024-09-23T16:45:59Z |
| format | Article |
| id | mit-1721.1/51374 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T16:45:59Z |
| publishDate | 2010 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/513742022-10-03T08:10:00Z Bayesian approach to cluster expansions Mueller, Timothy K. Ceder, Gerbrand Massachusetts Institute of Technology. Department of Materials Science and Engineering Ceder, Gerbrand Mueller, Timothy K. Ceder, Gerbrand Cluster expansions have proven to be a valuable tool in alloy theory and other problems in materials science but the generation of cluster expansions can be a computationally expensive and time-consuming process. We present a Bayesian framework for developing cluster expansions that explicitly incorporates physical insight into the fitting procedure. We demonstrate how existing methods fit within this framework and use the framework to develop methods that significantly improve the predictive power of cluster expansions for a given training set size. The key to the methods is to apply physical insight and cross validation to develop physically meaningful prior probability distributions for the cluster expansion coefficients. We use the Bayesian approach to develop an efficient method for generating cluster expansions for low-symmetry systems such as surfaces and nanoparticles. Department of Energy 2010-02-05T16:06:50Z 2010-02-05T16:06:50Z 2009-07 2009-04 Article http://purl.org/eprint/type/JournalArticle 1550-235X 1098-0121 http://hdl.handle.net/1721.1/51374 Mueller, Tim , and Gerbrand Ceder. “Bayesian approach to cluster expansions.” Physical Review B 80.2 (2009): 024103. (C) 2010 The American Physical Society. en_US http://dx.doi.org/10.1103/PhysRevB.80.024103 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 Bayesian approach to cluster expansions |
| title | Bayesian approach to cluster expansions |
| title_full | Bayesian approach to cluster expansions |
| title_fullStr | Bayesian approach to cluster expansions |
| title_full_unstemmed | Bayesian approach to cluster expansions |
| title_short | Bayesian approach to cluster expansions |
| title_sort | bayesian approach to cluster expansions |
| url | http://hdl.handle.net/1721.1/51374 |
| work_keys_str_mv | AT muellertimothyk bayesianapproachtoclusterexpansions AT cedergerbrand bayesianapproachtoclusterexpansions |