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We discuss some simple examples to show how these underlying justifying conditions can arise. Examples include brain simulation, combat attrition, and the greatly reduced computational complexity represented by Pascal\u2019s triangle. Homomorphism is also shown to be fundamental for constructing approximate low-resolution models. Models that simplify complex time-demanding simulation models are often used as surrogate or metamodels in system optimization. However, such models are fitted typically to computationally derived response surfaces and not structurally related directly to the originals using homomorphisms as described here. Along these lines, we show how homomorphism plays an essential role in a novel approach being developed to strongly control tree expansion in state space explorations of stochastic system simulation.<\/jats:p>","DOI":"10.1177\/00375497241264834","type":"journal-article","created":{"date-parts":[[2024,12,2]],"date-time":"2024-12-02T07:21:21Z","timestamp":1733124081000},"page":"1181-1196","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["The utility of homomorphism concepts in simulation: building families of models from base-lumped model pairs"],"prefix":"10.1177","volume":"100","author":[{"given":"Bernard P","family":"Zeigler","sequence":"first","affiliation":[{"name":"Department of Electrical & Computer Engineering, The University of Arizona, USA"},{"name":"RTSync Corporation, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Christian","family":"Koertje","sequence":"additional","affiliation":[{"name":"RTSync Corporation, USA"},{"name":"Department of Physics, University of Massachusetts Amherst, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Cole","family":"Zanni","sequence":"additional","affiliation":[{"name":"Department of Systems Science and Industrial Engineering, Binghamton University, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2024,12,2]]},"reference":[{"key":"bibr1-00375497241264834","doi-asserted-by":"publisher","DOI":"10.3390\/systems12030080"},{"key":"bibr2-00375497241264834","volume-title":"Theory of modeling and simulation","author":"Zeigler BP","year":"2018","edition":"3"},{"key":"bibr3-00375497241264834","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-031-11085-6"},{"key":"bibr4-00375497241264834","volume-title":"Multifacetted modelling and discrete event simulation","author":"Zeigler BP.","year":"1984"},{"key":"bibr5-00375497241264834","doi-asserted-by":"publisher","DOI":"10.1109\/WSC.2013.6721515"},{"key":"bibr6-00375497241264834","doi-asserted-by":"publisher","DOI":"10.3390\/info14040202"},{"key":"bibr7-00375497241264834","doi-asserted-by":"publisher","DOI":"10.1016\/B978-0-12-813543-3.00002-0"},{"key":"bibr8-00375497241264834","doi-asserted-by":"publisher","DOI":"10.3390\/app11114936"},{"key":"bibr9-00375497241264834","doi-asserted-by":"publisher","DOI":"10.1038\/311419a0"},{"key":"bibr10-00375497241264834","doi-asserted-by":"publisher","DOI":"10.1177\/0037549715611485"},{"key":"bibr11-00375497241264834","doi-asserted-by":"publisher","DOI":"10.1177\/1548512917717085"},{"key":"bibr12-00375497241264834","doi-asserted-by":"publisher","DOI":"10.23919\/SpringSim.2019.8732861"},{"key":"bibr13-00375497241264834","doi-asserted-by":"publisher","DOI":"10.3390\/app7101056"},{"key":"bibr14-00375497241264834","doi-asserted-by":"publisher","DOI":"10.1080\/03081077808960665"},{"key":"bibr15-00375497241264834","volume-title":"Proceedings of the symposium on theory of modeling & simulation","author":"Zeigler BP","year":"2013"},{"key":"bibr16-00375497241264834","doi-asserted-by":"publisher","DOI":"10.1177\/00375497231176085"},{"key":"bibr17-00375497241264834","doi-asserted-by":"publisher","DOI":"10.3390\/systems6040040"},{"key":"bibr18-00375497241264834","doi-asserted-by":"publisher","DOI":"10.1016\/j.jocs.2015.11.004"},{"key":"bibr19-00375497241264834","doi-asserted-by":"publisher","DOI":"10.1016\/j.cor.2012.08.022"},{"key":"bibr20-00375497241264834","doi-asserted-by":"publisher","DOI":"10.1016\/j.envsoft.2023.105639"},{"key":"bibr21-00375497241264834","doi-asserted-by":"publisher","DOI":"10.3389\/fnins.2018.00291"},{"key":"bibr22-00375497241264834","doi-asserted-by":"publisher","DOI":"10.1016\/S0246-0203(99)80006-5"},{"key":"bibr23-00375497241264834","doi-asserted-by":"publisher","DOI":"10.3389\/neuro.09.031.2009"},{"key":"bibr24-00375497241264834","unstructured":"Muzy A, Zeigler BP. 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