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Gerbrand Ceder. Huang, Wenxuan, Ph. D. Massachusetts Institute of Technology Massachusetts Institute of Technology. Department of Materials Science and Engineering. Massachusetts Institute of Technology. Department of Materials Science and Engineering 2018-05-23T16:31:06Z 2018-05-23T16:31:06Z 2017 2018 http://hdl.handle.net/1721.1/115705 1036986055 Thesis: Ph. D., Massachusetts Institute of Technology, Department of Materials Science and Engineering, February 2018. Cataloged from PDF version of thesis. Includes bibliographical references (pages 106-111). In this thesis, we propose strategies to solve the general ground state problem for arbitrary effective cluster interactions and construct ground state preserving cluster expansions. A full mathematical definition of our problem has been formalized to illustrate its generality and clarify our discussion. We review previous methods in material science community: Monte Carlo based method, configurational polytope method, and basic ray method. Further, we investigate the connection of the ground state problem with deeper mathematical results about computational complexity and NP-hard combinatorial optimization (MAX-SAT). We have proposed a general scheme, upper bound and lower bound calculation to approach this problem. Firstly, based on the traditional configurational polytope method, we have proposed a method called cluster tree optimization method, which eliminates the necessity of introducing an exponential number of variables to counter frustration, and thus significantly improves tractability. Secondly, based on convex optimization and finite optimization without periodicity, we have introduced a beautiful MAX-MIN method to refine lower bound calculation. Finally, we present a systematic and mathematically sound method to obtain cluster expansion models that are guaranteed to preserve the ground states of the reference data. by Wenxuan Huang. Ph.D. 111 pages eng Massachusetts Institute of Technology MIT theses are protected by copyright. They may be viewed, downloaded, or printed from this source but further reproduction or distribution in any format is prohibited without written permission. http://dspace.mit.edu/handle/1721.1/7582 Materials Science and Engineering. Ground state determination, ground state preserving fit for cluster expansion and their integration for robust CE construction Thesis application/pdf false Publication unknown unknown <Publication xmlns="https://www.openaire.eu/cerif-profile/1.1/" id="98f67a1b-72a1-4418-b9e3-f727cd319e9d"> <Type xmlns="https://www.openaire.eu/cerif-profile/vocab/COAR_Publication_Types">http://purl.org/coar/resource_type/c_1843</Type> <Language>eng</Language> <Title>Ground state determination, ground state preserving fit for cluster expansion and their integration for robust CE construction</Title> <PublishedIn> <Publication> </Publication> </PublishedIn> <PublicationDate>2018</PublicationDate> <Authors> <Author> <DisplayName>Huang, Wenxuan, Ph. D. Massachusetts Institute of Technology</DisplayName> <Affiliation> <OrgUnit> </OrgUnit> </Affiliation> </Author> </Authors> <Editors> </Editors> <Publishers> <Publisher> <DisplayName>Massachusetts Institute of Technology</DisplayName> <OrgUnit /> </Publisher> </Publishers> <License>http://dspace.mit.edu/handle/1721.1/7582</License> <Keyword>Materials Science and Engineering.</Keyword> <Abstract>In this thesis, we propose strategies to solve the general ground state problem for arbitrary effective cluster interactions and construct ground state preserving cluster expansions. A full mathematical definition of our problem has been formalized to illustrate its generality and clarify our discussion. We review previous methods in material science community: Monte Carlo based method, configurational polytope method, and basic ray method. Further, we investigate the connection of the ground state problem with deeper mathematical results about computational complexity and NP-hard combinatorial optimization (MAX-SAT). We have proposed a general scheme, upper bound and lower bound calculation to approach this problem. Firstly, based on the traditional configurational polytope method, we have proposed a method called cluster tree optimization method, which eliminates the necessity of introducing an exponential number of variables to counter frustration, and thus significantly improves tractability. Secondly, based on convex optimization and finite optimization without periodicity, we have introduced a beautiful MAX-MIN method to refine lower bound calculation. Finally, we present a systematic and mathematically sound method to obtain cluster expansion models that are guaranteed to preserve the ground states of the reference data.</Abstract> <Access xmlns="http://purl.org/coar/access_right" > </Access> </Publication>