Koopman-based Data-driven Soft Artificial Life: Obtaining Rulesets from observed data

Koopman-based Data-driven Soft Artificial Life: Obtaining Rulesets from Observed Data | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Koopman-based Data-driven Soft Artificial Life: Obtaining Rulesets from Observed Data Saumitra Dwivedi, Ricardo da Silva Torres, Ibrahim A. Hameed, and 2 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4995759/v2 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 06 Aug, 2025 Read the published version in Natural Computing → Version 2 posted 6 You are reading this latest preprint version Show more versions Abstract Software-based artificial life methods use mathematical and computational models to mimic complexity in living systems. Although such methods seem promising pertaining to exploring emergent behaviour, obtaining the governing rulesets of such methods remains challenging. In this paper, we present a concept of combined use of methods targeting different levels/scales in an emergent behaviour to obtain software-based artificial life rulesets from observed data. Additionally, we investigate the consequences of using this combination of methods by proposing an instance of combining Cellular Automata (CA) and Agent-based modelling (ABM) with Koopman-based linearization. Our experiments on systems of Elementary Cellular Automaton (Rule 30), Game of Life (GOL), and Vicsek’s flocking show that the combined method can learn the overall non-linear and emergent behaviour, and the underlying governing rulesets. Our research also indicates that by identifying several emergent scales or levels in a system, the combined method has the potential to shed light on the learnt system dynamics. Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 06 Aug, 2025 Read the published version in Natural Computing → Version 2 posted Editorial decision: Accepted 17 Jul, 2025 Reviews received at journal 15 Jul, 2025 Reviewers agreed at journal 07 Jul, 2025 Reviewers invited by journal 04 Jul, 2025 Submission checks completed at journal 02 Jul, 2025 First submitted to journal 02 Jul, 2025 You are reading this latest preprint version Show more versions Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4995759","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":484943418,"identity":"6583655a-5ee7-4c0d-932e-c8c5ec0d36f7","order_by":0,"name":"Saumitra Dwivedi","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA70lEQVRIiWNgGAWjYLCCBCh5gIGBmYefOC0JSFokG5iJtgZMMDMYHCCgRb79jOmGhz/uyTOw5xge5qmwljG+3X/sMQ/DHTlcWgzO5JjdSEgoNmzgeWNwmOdMOo/ZncPsxjwMz4xxamEAa0lgbJDI3XBwZtthHrMbyWzSPAyHExtwOaz/DViLPUTLv8M8xjMIaGG4AbElEaTlwMeGwzwGEgS0GNx4VnYjIS0huY3n/YcDH46l80jcSDaTnGNwGKdf5PuTt938YZNg28+elvwhocbann9G4jOJNxWHcYYYHLCh2U5QwygYBaNgFIwCPAAAhoFX0KPgVGgAAAAASUVORK5CYII=","orcid":"","institution":"Norwegian University of Science and Technology","correspondingAuthor":true,"prefix":"","firstName":"Saumitra","middleName":"","lastName":"Dwivedi","suffix":""},{"id":484943419,"identity":"92f99af9-532f-405f-b53c-3bc3d37e6fc3","order_by":1,"name":"Ricardo da Silva Torres","email":"","orcid":"","institution":"Wageningen University \u0026 Research","correspondingAuthor":false,"prefix":"","firstName":"Ricardo","middleName":"da Silva","lastName":"Torres","suffix":""},{"id":484943420,"identity":"8587672c-95bc-4919-a4a9-38aaf66dc7c6","order_by":2,"name":"Ibrahim A. Hameed","email":"","orcid":"","institution":"Norwegian University of Life Sciences (NMBU)","correspondingAuthor":false,"prefix":"","firstName":"Ibrahim","middleName":"A.","lastName":"Hameed","suffix":""},{"id":484943421,"identity":"7f4ba873-40c7-414e-a6c7-36ea7479665c","order_by":3,"name":"Gunnar Tufte","email":"","orcid":"","institution":"Norwegian University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Gunnar","middleName":"","lastName":"Tufte","suffix":""},{"id":484943422,"identity":"114f0d0b-d701-4c34-b58b-1117540adec4","order_by":4,"name":"Anniken Susanne T. Karlsen","email":"","orcid":"","institution":"Norwegian University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Anniken","middleName":"Susanne T.","lastName":"Karlsen","suffix":""}],"badges":[],"createdAt":"2024-08-29 08:07:12","currentVersionCode":2,"declarations":"","doi":"10.21203/rs.3.rs-4995759/v2","doiUrl":"https://doi.org/10.21203/rs.3.rs-4995759/v2","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s11047-025-10042-9","type":"published","date":"2025-08-07T00:00:00+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":88633401,"identity":"f58ab45d-d7ad-4f62-b8af-63a7273f809e","added_by":"auto","created_at":"2025-08-08 14:25:59","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2421937,"visible":true,"origin":"","legend":"","description":"","filename":"SaumitraDwivediNaturalComputingv5.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4995759/v2_covered_bd6a5639-8f4e-436c-bb76-7026c2f72b82.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Koopman-based Data-driven Soft Artificial Life: Obtaining Rulesets from Observed Data","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"natural-computing","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"naco","sideBox":"Learn more about [Natural Computing](http://link.springer.com/journal/11047)","snPcode":"11047","submissionUrl":"https://submission.nature.com/new-submission/11047/3","title":"Natural Computing","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-4995759/v2","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4995759/v2","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Software-based artificial life methods use mathematical and computational models to mimic complexity in living systems. Although such methods seem promising pertaining to exploring emergent behaviour, obtaining the governing rulesets of such methods remains challenging. In this paper, we present a concept of combined use of methods targeting different levels/scales in an emergent behaviour to obtain software-based artificial life rulesets from observed data. Additionally, we investigate the consequences of using this combination of methods by proposing an instance of combining Cellular Automata (CA) and Agent-based modelling (ABM) with Koopman-based linearization. Our experiments on systems of Elementary Cellular Automaton (Rule 30), Game of Life (GOL), and Vicsek’s flocking show that the combined method can learn the overall non-linear and emergent behaviour, and the underlying governing rulesets. Our research also indicates that by identifying several emergent scales or levels in a system, the combined method has the potential to shed light on the learnt system dynamics.","manuscriptTitle":"Koopman-based Data-driven Soft Artificial Life: Obtaining Rulesets from Observed Data","msid":"","msnumber":"","nonDraftVersions":[{"code":2,"date":"2025-07-15 11:44:56","doi":"10.21203/rs.3.rs-4995759/v2","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Accepted","date":"2025-07-17T07:27:05+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-07-15T17:08:00+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"333300701995017580552001727974681759870","date":"2025-07-07T14:49:26+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-07-04T07:17:24+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-07-03T03:19:05+00:00","index":"","fulltext":""},{"type":"submitted","content":"Natural Computing","date":"2025-07-02T12:52:45+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"natural-computing","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"naco","sideBox":"Learn more about [Natural Computing](http://link.springer.com/journal/11047)","snPcode":"11047","submissionUrl":"https://submission.nature.com/new-submission/11047/3","title":"Natural Computing","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}},{"code":1,"date":"2025-05-22 13:34:30","doi":"10.21203/rs.3.rs-4995759/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-06-22T16:37:27+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-01-05T21:18:02+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"292015636293111357272710809610436868491","date":"2024-12-18T16:27:14+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"333300701995017580552001727974681759870","date":"2024-11-09T02:34:54+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-11-05T16:19:18+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-10-21T10:28:24+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-08-31T05:50:04+00:00","index":"","fulltext":""},{"type":"submitted","content":"Natural Computing","date":"2024-08-29T08:05:54+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"natural-computing","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"naco","sideBox":"Learn more about [Natural Computing](http://link.springer.com/journal/11047)","snPcode":"11047","submissionUrl":"https://submission.nature.com/new-submission/11047/3","title":"Natural Computing","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"5a2403a7-5e6f-4ee4-a362-7d853cb74429","owner":[],"postedDate":"July 15th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2025-08-08T14:25:51+00:00","versionOfRecord":{"articleIdentity":"rs-4995759","link":"https://doi.org/10.1007/s11047-025-10042-9","journal":{"identity":"natural-computing","isVorOnly":false,"title":"Natural Computing"},"publishedOn":"2025-08-07 00:00:00","publishedOnDateReadable":"August 7th, 2025"},"versionCreatedAt":"2025-07-15 11:44:56","video":"","vorDoi":"10.1007/s11047-025-10042-9","vorDoiUrl":"https://doi.org/10.1007/s11047-025-10042-9","workflowStages":[]},"version":"v2","identity":"rs-4995759","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4995759","identity":"rs-4995759","version":["v2"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}