Encoding multiphase dynamics to predict spatiotemporal evolution via latent-space operators

Encoding multiphase dynamics to predict spatiotemporal evolution via latent-space operators | 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 Encoding multiphase dynamics to predict spatiotemporal evolution via latent-space operators Xinliang Li, Hongyuan Men, Yixuan Mao, Vito Tagarielli, Francesco Montomoli, and 2 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7733480/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 Modeling complex multiphase flows relies on solving partial differential equations (PDEs) that capture the intricate transfers of mass, momentum, and energy among the interacting phases. These systems typically involve intricate couplings between gas, liquid, and solid phases, exhibiting dynamics that diverge from those of single-phase flows. We present MultiOKAN, a novel deep learning framework that integrate a Kolmogorov-Arnold autoencoder with a latent-space operator network to approximate the mappings from initial state to future evolution, which aims to substitute traditional PDEs solver. The encoder compresses initial volume fraction fields into a low-dimensional latent representation, which is fed into operator to predict the future morphology evolution. Systematic comparisons of bubble rise, particle deposition, and fluidized bed demonstrate that the width of layer dominates encoder fidelity, whereas operator accuracy depends on balancing expressiveness and overfitting. In addition, compared with fully connected and convolutional baselines, MultiOKAN reduces the reconstruction error by a significant margin while maintaining a similar computational cost. Latent projection also endows the model with strong resilience to noise and modest data budgets, preserving accuracy even under substantial perturbations or when trained on a fraction of the original samples. One of the important features of current framework is its multiphase compatibility with new structured latent representation acquisition strategies. This work opens a promising pathway toward leveraging neural operators for real-time spatiotemporal prediction of multiphase systems. Physical sciences/Mathematics and computing/Computational science Physical sciences/Physics/Fluid dynamics Full Text Additional Declarations There is NO Competing Interest. Supplementary Files supplimentary.pdf Encoding multiphase dynamics to predict spatiotemporal evolution via latent-space operators 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-7733480","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":526561898,"identity":"7c43e411-5ace-4309-96ce-0adedcd688c8","order_by":0,"name":"Xinliang 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