Physics-Informed Neural Networks Reveal Interpretable Mechanisms of Multi-Ethnic Urban Settlement Dynamics

Physics-Informed Neural Networks Reveal Interpretable Mechanisms of Multi-Ethnic Urban Settlement Dynamics | 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 Article Physics-Informed Neural Networks Reveal Interpretable Mechanisms of Multi-Ethnic Urban Settlement Dynamics Seyed Navid Mashhadi Moghaddam, Huhua Cao, Michael Sawada This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8800188/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted You are reading this latest preprint version Abstract Ethnic enclaves are widely assumed to reflect self-reinforcing segregation, yet no existing framework can mechanistically distinguish whether observed settlement patterns arise from group-specific isolation, multi-ethnic attraction, or historical contingency operating within a multi-stable dynamical landscape. Here we introduce GraphPDE, a physics-informed graph neural network that embeds coupled multi-ethnic reaction-diffusion dynamics on neighbourhood-level spatial graphs, jointly learning interpretable demographic parameters, diffusion coefficients, growth rates, carrying capacities, and inter-group interaction matrices, directly from two decades of census observations across major Canadian cities. The learned dynamics reveal that ethnic settlement constitutes a non-equilibrium, multi-stable, group-specific dynamical system governed by pattern formation principles previously documented only in physical and biological contexts. Settlement morphologies traverse a crystallization sequence from spots through stripes to labyrinthine networks; nucleation thresholds and spatial mobility scales vary by more than an order of magnitude across groups, invalidating ethnicity-invariant assumptions in classical models; and multi-stability analysis demonstrates that extreme segregation is energetically disfavoured while integration proceeds most naturally through intermediate multi-ethnic bridging configurations. Critically, the learned interaction matrices show that the most spatially concentrated communities persist not through self-isolation but through cross-group attraction, fundamentally reframing the segregation-integration debate. Evaluated across multiple forecasting horizons up to two decades and validated on an independent traffic forecasting benchmark, GraphPDE achieves state-of-the-art multi-step predictive stability while providing mechanistic interpretability that post-hoc explanation methods cannot deliver, offering a general paradigm for embedding partially known governing equations into graph-based learning architectures across scientific domains. Scientific community and society/Geography Scientific community and society/Social sciences/Society Physical sciences/Mathematics and computing/Scientific data Earth and environmental sciences/Environmental social sciences/Socioeconomic scenarios Full Text Additional Declarations There is NO Competing Interest. Supplementary Files nrreportingsummary.pdf Article File - Reporting Summary MLCheckList.pdf Article File - Machine learning checklist nrsoftwarepolicy.pdf Article File - Software policy Cite Share Download PDF Status: Under Review Version 1 posted You are reading this latest preprint version 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-8800188","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":590783338,"identity":"5bf2d289-6d1a-44b6-89cc-367c19c32958","order_by":0,"name":"Seyed Navid Mashhadi Moghaddam","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA30lEQVRIie3NrwrCUBTH8bPiygXrTL7CvQzEoPggFsdgaQOjwXBB0KZ1YQ8xEJbPGLgyWR3cIgimhSWjuvkHTNdFw/2mXzgfDoBK9YdRBEBSj25rMvyQHgeNYxsyaq7I611bkmYMS4imZmGn52qZ9EFPTlIyyFwaByC8qHAsjoeEceJQOUFnlpAncRnHjtC4AXJi5pcX2fsNuYkJN/RKSlhh45OERk3itbC4QeRfWHHGOKDC87OL5R+3d3tN3LmU0NxaVeVCeLuNjdXi6ox3ehpKyRt+7U6Le5VKpVL96AHRClak/moA1AAAAABJRU5ErkJggg==","orcid":"","institution":"University of Ottawa","correspondingAuthor":true,"prefix":"","firstName":"Seyed","middleName":"Navid Mashhadi","lastName":"Moghaddam","suffix":""},{"id":590783339,"identity":"37588bfe-dbb9-4b7a-91cb-92cbb377dd32","order_by":1,"name":"Huhua Cao","email":"","orcid":"","institution":"University of Ottawa","correspondingAuthor":false,"prefix":"","firstName":"Huhua","middleName":"","lastName":"Cao","suffix":""},{"id":590783340,"identity":"52ed79a0-1604-4b78-87ac-e11412c0005b","order_by":2,"name":"Michael Sawada","email":"","orcid":"","institution":"University of Ottawa","correspondingAuthor":false,"prefix":"","firstName":"Michael","middleName":"","lastName":"Sawada","suffix":""}],"badges":[],"createdAt":"2026-02-05 18:51:07","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8800188/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8800188/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":102751189,"identity":"cb678959-a158-44a0-8f90-2aae35f893ff","added_by":"auto","created_at":"2026-02-16 09:24:04","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":6927325,"visible":true,"origin":"","legend":"","description":"","filename":"manuscriptfinalv2.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8800188/v1_covered_f0e1a38e-a8e3-418b-9819-e09a2aedb920.pdf"},{"id":102749151,"identity":"ee0872cc-5ff5-4312-a703-f14cde4ccaa4","added_by":"auto","created_at":"2026-02-16 09:12:07","extension":"pdf","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":1665796,"visible":true,"origin":"","legend":"Article File - 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