[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-84210-en":3,"doc-seo-84210-105":29,"detail-sidebar-cat-0-en-105":90},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},84210,962075114765,"Quinn","https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd",8,"Research & Report","BubbleSH: A Dataset of Rising Bubbles with Deformable Interfaces","Bubbly flows feature multiscale behavior where deformable bubbles interact through the surrounding liquid, producing tightly coupled kinematics and morphology. BubbleSH provides a publicly available dataset of transient, three-dimensional bubble-swarm dynamics generated by high-fidelity direct numerical simulations in a periodic domain. The data include time-resolved trajectories, velocities, and shape evolution, with compact morphology encoding via spherical harmonics. The work defines evaluation metrics for trajectory and shape prediction and tests an equivariant probabilistic emulator.","arXiv :2607 .07275v 1 [ cs .LG] 8 Jul 2026  \nBubbleSH: A Dataset of Rising Bubbles with Deformable Interfaces  \nRachna Ramesh 1 Kiet Bennema ten Brinke 1 Douwe Orij2 Ivo Roghair2  \nVlado Menkovski 1  \n1 Department of Mathematics and Computer Science, Eindhoven University of Technology  \n2 Department of Chemical Engineering and Chemistry, Eindhoven University of Technology {r.ramesh1, k.bennema.ten.brinke, d.r.orij, i.roghair, [v.menkovski}@tue.nl](v.menkovski}@tue.nl)  \nAbstract  \nBubbly flows exhibit complex multiscale dynamics, with deformable bubbles interacting through the surrounding liquid and giving rise to strongly coupled kinematic and morphological behavior. We present BubbleSH, a bubbly flows dataset consisting of transient, three-dimensional bubble-swarm dynamics obtained from high-fidelity direct numerical simulations of bubbles rising in a periodic domain. The dataset provides time-resolved bubble trajectories, velocities, and shape evolution, with bubble morphology compactly represented using spherical harmonics. Designed to be lightweight yet physically expressive, the dataset enables data-driven modeling of bubbly flow simulators where shape deformation and bubble–bubble interactions play a central role. We characterize the dataset with bubble kinematics, morphology, and interaction patterns, and introduce evaluation metrics for both trajectory and shape prediction. The sensitivity of bubble-swarm dynamics to local perturbations makes BubbleSH particularly well suited to generative models that learn distributions over possible future trajectories. We evaluate apermutationally and translationally equivariant probabilistic emulator on BubbleSH given the proposed metrics. Therefore, we establish a compact, high-fidelity dataset and a benchmark for developing and evaluating data-driven models of deformable, chaotic multiphase systems. The dataset is publicly available on Zenodo under DOI: [https://doi.org/10.5281/zenodo.21229301](https://doi.org/10.5281/zenodo.21229301) .  \n1 Introduction  \nBubbly flows, which consist of gas bubbles that rise through a liquid, occur in a wide range of natural and industrial systems. They play a central role in chemical and biochemical reactors, metallurgical processes, wastewater treatment, and many other applications. In bubble swarms, rising bubbles influence each other’s trajectories, generate turbulence, induce macroscopic circulation patterns in the surrounding liquid and affect mass, momentum and energy exchange between phases. A detailed understanding of bubble motion, deformation, and interactions within swarms is essential to design efficient reactors, improve scale-up methodologies, and advance predictive simulation tools.  \nObtaining such insights experimentally remains extremely challenging due to optical occlusion and dense multiphase interactions, especially at higher gas fractions. For this reason, significant emphasis has been placed on numerical approaches, in particular Direct Numerical Simulations (DNS), with modern interface-resolving methods such as Volume-of-Fluid (VoF) [16, 44, 26, 41] and Front-Tracking (FT) [40, 42, 28] . The FT method explicitly tracks deformable bubble interfaces and avoids the (unphysical) numerical coalescence present in VoF schemes. FT has been demonstrated to reproduce complex bubble interaction behavior, for instance wobbling bubbles and path instabilities [10, 11], bubble–bubble interactions and swarm statistics [30, 5, 6, 37], turbulence generation [29],  \nPreprint.  \nand providing physically consistent drag forces [27] and mass transfer rates [8, 28] over a wide range of gas fractions.  \nWhile Direct Numerical Simulations (DNS) provide an exceptional level of detail, their applicability is limited to small scales due to computational cost. Larger-scale simulations therefore rely on Euler–Lagrange (EL) models, which describe the liquid phase through detailed closures but approximate the bubble phase using time-averaged correlation","cbCaitLufkh87rlR","https://ap.wps.com/l/cbCaitLufkh87rlR","pdf",2911751,1,17,"English","en",105,"# Abstract\n# Introduction\n## Background and applications of bubbly flows\n## Challenges in experimental observation\n## Numerical simulation approaches (VoF and FT)\n## Limitations of DNS and need for data-driven datasets\n## Contribution: BubbleSH dataset and benchmark design","[{\"question\":\"What does the BubbleSH dataset provide?\",\"answer\":\"BubbleSH provides time-resolved three-dimensional bubble-swarm dynamics, including bubble trajectories, velocities, and shape evolution derived from high-fidelity direct numerical simulations.\"},{\"question\":\"How is bubble morphology represented in the dataset?\",\"answer\":\"Bubble morphology is compactly represented using spherical harmonics coefficients, computed from simulated interface meshes.\"},{\"question\":\"Why is BubbleSH suitable for generative or probabilistic modeling?\",\"answer\":\"Bubble-swarm dynamics are sensitive to local perturbations, and the dataset includes coupled shape deformation and bubble–bubble interactions, enabling models that learn distributions over future trajectories. The paper evaluates an equivariant probabilistic emulator using proposed metrics.\"}]",1784193992,43,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":85,"head_meta":87,"extra_data":89,"updated_unix":27},"bubblesh-a-dataset-of-rising-bubbles-with-deformable-interfaces","",{"@graph":35,"@context":84},[36,53,67],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/bubblesh-a-dataset-of-rising-bubbles-with-deformable-interfaces/84210/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":61,"encodingFormat":60,"isAccessibleForFree":62,"interactionStatistic":63},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-16",true,{"@type":64,"interactionType":65,"userInteractionCount":4},"InteractionCounter",{"@type":66},"ViewAction",{"@type":68,"mainEntity":69},"FAQPage",[70,76,80],{"name":71,"@type":72,"acceptedAnswer":73},"What does the BubbleSH dataset provide?","Question",{"text":74,"@type":75},"BubbleSH provides time-resolved three-dimensional bubble-swarm dynamics, including bubble trajectories, velocities, and shape evolution derived from high-fidelity direct numerical simulations.","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"How is bubble morphology represented in the dataset?",{"text":79,"@type":75},"Bubble morphology is compactly represented using spherical harmonics coefficients, computed from simulated interface meshes.",{"name":81,"@type":72,"acceptedAnswer":82},"Why is BubbleSH suitable for generative or probabilistic modeling?",{"text":83,"@type":75},"Bubble-swarm dynamics are sensitive to local perturbations, and the dataset includes coupled shape deformation and bubble–bubble interactions, enabling models that learn distributions over future trajectories. The paper evaluates an equivariant probabilistic emulator using proposed metrics.","https://schema.org",{"og:url":51,"og:type":86,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":88,"canonical":51},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":91},[92,96,100,104,109,114,119,122,127,130,134],{"id":20,"doc_module":4,"doc_module_name":45,"category_name":93,"show_sort_weight":94,"slug":95},"Story & Novel",90,"story-novel",{"id":46,"doc_module":4,"doc_module_name":45,"category_name":97,"show_sort_weight":98,"slug":99},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":45,"category_name":101,"show_sort_weight":102,"slug":103},"Exam",70,"exam",{"id":105,"doc_module":4,"doc_module_name":45,"category_name":106,"show_sort_weight":107,"slug":108},5,"Comic",60,"comic",{"id":110,"doc_module":4,"doc_module_name":45,"category_name":111,"show_sort_weight":112,"slug":113},6,"Technology",50,"technology",{"id":115,"doc_module":4,"doc_module_name":45,"category_name":116,"show_sort_weight":117,"slug":118},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":45,"category_name":12,"show_sort_weight":120,"slug":121},30,"research-report",{"id":123,"doc_module":4,"doc_module_name":45,"category_name":124,"show_sort_weight":125,"slug":126},9,"Religion & Spirituality",20,"religion-spirituality",{"id":125,"doc_module":4,"doc_module_name":45,"category_name":128,"show_sort_weight":125,"slug":129},"World Cup","world-cup",{"id":131,"doc_module":4,"doc_module_name":45,"category_name":132,"show_sort_weight":131,"slug":133},10,"Lifestyle","lifestyle",{"id":135,"doc_module":4,"doc_module_name":45,"category_name":136,"show_sort_weight":105,"slug":137},19,"General","general"]