{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:38:54Z","timestamp":1787330334778,"version":"build-2736575974"},"reference-count":76,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","funder":[{"DOI":"10.13039\/501100018781","name":"Leverhulme Research Centre for Functional Materials Design","doi-asserted-by":"publisher","award":["EP\/R018472\/1"],"award-info":[{"award-number":["EP\/R018472\/1"]}],"id":[{"id":"10.13039\/501100018781","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100018781","name":"Leverhulme Research Centre for Functional Materials Design","doi-asserted-by":"publisher","award":["EP\/X018474\/1"],"award-info":[{"award-number":["EP\/X018474\/1"]}],"id":[{"id":"10.13039\/501100018781","id-type":"DOI","asserted-by":"publisher"}]},{"name":"RAEng fellowship","award":["IF2122\/186"],"award-info":[{"award-number":["IF2122\/186"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2023,8,31]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>Molecular crystal structure prediction (CSP) seeks the most stable periodic structure given the chemical composition of molecule and pressure-temperature conditions. Modern CSP solvers use global optimization methods to search for structures with minimal free energy within a complex energy landscape induced by intermolecular potentials. A major caveat of these methods is that initial configurations are random, making the search susceptible to convergence at local minima. Providing initial configurations that are densely packed with respect to the geometric representation of a molecule can significantly accelerate CSP. Motivated by these observations, we define a class of periodic packings restricted to crystallographic symmetry groups (CSG) and design a search method for the densest CSG packings in an information-geometric framework. Since CSG induces a toroidal topology on the configuration space, a non-Euclidean trust region method is performed on a statistical manifold consisting of probability distributions defined on an [Formula: see text]-dimensional flat unit torus by extending the multivariate von Mises distribution. Introducing an adaptive quantile reformulation of the fitness function into the optimization schedule provides the algorithm with a geometric characterization through local dual geodesic flows. Moreover, we examine the geometry of the adaptive selection-quantile defined trust region and show that the algorithm performs a maximization of stochastic dependence among elements of the extended multivariate von Mises distributed random vector. We experimentally evaluate the behavior and performance of the algorithm on various densest packings of convex polygons in 2-dimensional CSGs for which optimal solutions are known, and we demonstrate its application in the pentacene thin-film CSP.<\/jats:p>","DOI":"10.1137\/22m147983x","type":"journal-article","created":{"date-parts":[[2023,7,19]],"date-time":"2023-07-19T04:19:22Z","timestamp":1689740362000},"page":"B493-B522","source":"Crossref","is-referenced-by-count":1,"title":["Entropic Trust Region for Densest Crystallographic Symmetry Group Packings"],"prefix":"10.1137","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2115-7811","authenticated-orcid":true,"given":"Miloslav","family":"Torda","sequence":"first","affiliation":[{"name":"Leverhulme Research Centre for Functional Materials Design, University of Liverpool, Liverpool L73NY, UK."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"John Y.","family":"Goulermas","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Liverpool, Liverpool L693DR, UK."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Roland","family":"P\u00fa\u010dek","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Friedrich Schiller University Jena, Jena 07743, Germany."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5328-5351","authenticated-orcid":true,"given":"Vitaliy","family":"Kurlin","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Liverpool, Liverpool L693DR, UK."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2023,7,19]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1162\/089976698300017746"},{"key":"ref2","volume-title":"Methods of Information Geometry","author":"Amari S.-i.","year":"2000"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-76657-3_16"},{"key":"ref4","volume-title":"International Tables for Crystallography, Volume A: Space-Group Symmetry","author":"Aroyo M. I.","year":"2017","edition":"6"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.86.031302"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1020107773"},{"key":"ref7","first-page":"517","volume":"42","author":"Ay N.","year":"2006","journal-title":"Kybernetika"},{"key":"ref8","first-page":"1705","volume":"6","author":"Banerjee A.","year":"2005","journal-title":"J. Mach. Learn. Res."},{"key":"ref9","doi-asserted-by":"crossref","unstructured":"O. Barndorff-Nielsen , Information and Exponential Families in Statistical Theory, reprint of the 1978 original, Wiley Ser. Probab. Statist., John Wiley & Sons, 2014.","DOI":"10.1002\/9781118445112.stat00970"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-6377(02)00231-6"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1016\/S0925-7721(00)00007-9"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-04378-3"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1162\/EVCO_a_00132"},{"key":"ref14","series-title":"Colloquia Mathematica Sociates J\u00e1nos B\u00f3lyai 63","first-page":"17","volume-title":"Intuitive Geometry","author":"Bezdek A.","year":"1994"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1016\/0041-5553(67)90040-7"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1107\/S0365110X61002163"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1007\/BF00940051"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1039\/b805788e"},{"key":"ref19","volume-title":"Probabilistic Networks and Expert Systems: Exact Computational Methods for Bayesian Networks","author":"Cowell R. G.","year":"1999"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1021\/acs.nanolett.8b03126"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1038\/s41928-021-00670-1"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1063\/1.4767529"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1021\/nn3007948"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.3390\/e22010101"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1007\/s00205-015-0862-1"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1080\/0892702031000104887"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1007\/s11222-017-9790-2"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.1984.4767596"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9868.2010.00765.x"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1016\/j.cpc.2006.07.020"},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.1002\/jcc.21057"},{"key":"ref32","unstructured":"T. Hales  and \nW. Kusner , Packings of Regular Pentagons in the Plane, preprint, arXiv:1602.07220, 2016."},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.4007\/annals.2005.162.1065"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1162\/106365601750190398"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/67.1.163"},{"key":"ref36","doi-asserted-by":"publisher","DOI":"10.1214\/lnms\/1215467061"},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4419-9982-5"},{"key":"ref38","doi-asserted-by":"publisher","DOI":"10.4171\/emss\/13"},{"key":"ref39","doi-asserted-by":"publisher","DOI":"10.1162\/neco.1997.9.8.1661"},{"key":"ref40","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1111\/j.2517-6161.1975.tb01550.x","volume":"37","author":"Mardia K. V.","year":"1975","journal-title":"J. R. Stat. Soc. Ser. B Methodol."},{"key":"ref41","doi-asserted-by":"publisher","DOI":"10.1002\/cjs.5550360110"},{"key":"ref42","doi-asserted-by":"publisher","DOI":"10.1021\/ja400881n"},{"key":"ref43","volume-title":"Symmetry Groups and Their Applications","author":"Miller W.","year":"1973"},{"key":"ref44","first-page":"245","volume":"6","author":"Mount D. M.","year":"1991","journal-title":"Discrete Comput. Geom."},{"key":"ref45","doi-asserted-by":"publisher","DOI":"10.1016\/0196-6774(90)90010-C"},{"key":"ref46","doi-asserted-by":"publisher","DOI":"10.1021\/acs.jpcc.7b02480"},{"key":"ref47","volume-title":"Problem Complexity and Method Efficiency in Optimization","author":"Nemirovskij A. S.","year":"1983"},{"key":"ref48","volume-title":"Numerical Optimization","author":"Nocedal J.","year":"2006","edition":"2"},{"key":"ref49","first-page":"564","volume":"18","author":"Ollivier Y.","year":"2017","journal-title":"J. Mach. Learn. Res."},{"key":"ref50","doi-asserted-by":"publisher","DOI":"10.1039\/C8FD00121A"},{"key":"ref51","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2015.2388583"},{"key":"ref52","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-02431-3"},{"key":"ref53","doi-asserted-by":"publisher","DOI":"10.1007\/BF02392671"},{"key":"ref54","volume-title":"Packing and Covering","author":"Rogers C. A.","year":"1964"},{"key":"ref55","doi-asserted-by":"publisher","DOI":"10.1021\/jp953141+"},{"key":"ref56","doi-asserted-by":"publisher","DOI":"10.1039\/C7NR00703E"},{"key":"ref57","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.71.036138"},{"key":"ref58","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.1980.1056144"},{"key":"ref59","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/89.3.719"},{"key":"ref60","doi-asserted-by":"publisher","DOI":"10.1063\/1.1760076"},{"key":"ref61","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-011-5014-9_10"},{"key":"ref62","doi-asserted-by":"publisher","DOI":"10.1287\/moor.17.3.670"},{"key":"ref63","doi-asserted-by":"publisher","DOI":"10.1007\/s00220-005-1458-7"},{"key":"ref64","doi-asserted-by":"publisher","DOI":"10.1063\/1.5036657"},{"key":"ref65","volume-title":"Handbook of Discrete and Computational Geometry","author":"Toth C. D.","year":"2017"},{"key":"ref66","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-65234-9"},{"key":"ref67","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-015-7744-1"},{"key":"ref68","doi-asserted-by":"publisher","DOI":"10.1146\/annurev-physchem-050317-021219"},{"key":"ref69","doi-asserted-by":"publisher","DOI":"10.1002\/ange.202010805"},{"key":"ref70","doi-asserted-by":"publisher","DOI":"10.1006\/jsbi.1999.4161"},{"key":"ref71","doi-asserted-by":"publisher","DOI":"10.1147\/rd.41.0066"},{"key":"ref72","doi-asserted-by":"crossref","unstructured":"D. Widdowson  and \nV. Kurlin , Resolving the data ambiguity for periodic crystals, in Proceedings of the 36th Conference on Neural Information Processing Systems (NeurIPS 2022), Advances Neural Inform. Proc. Systems 35, Curran Associates, 2022, pp. 24625\u201324638.","DOI":"10.52202\/068431-1788"},{"key":"ref73","doi-asserted-by":"publisher","DOI":"10.46793\/match.87-3.529W"},{"key":"ref74","first-page":"949","volume":"15","author":"Wierstra D.","year":"2014","journal-title":"J. Mach. Learn. Res."},{"key":"ref75","doi-asserted-by":"publisher","DOI":"10.1098\/rsta.2019.0600"},{"key":"ref76","doi-asserted-by":"publisher","DOI":"10.1021\/acs.jpclett.5b02147"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/22M147983X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T15:58:36Z","timestamp":1787327916000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/22M147983X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,7,19]]},"references-count":76,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2023,8,31]]}},"alternative-id":["10.1137\/22M147983X"],"URL":"https:\/\/doi.org\/10.1137\/22m147983x","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,7,19]]}}}