{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/hidden-fluid-mechanics-a-navier-stokes","title":"Hidden Fluid Mechanics: A Navier-Stokes Informed Deep Learning Framework for Assimilating Flow Visualization Data","arxiv_id":"1808.04327","date":"2018-08-13","proceeding":null,"authors":["Maziar Raissi","Alireza Yazdani","George Em. Karniadakis"],"abstract":"We present hidden fluid mechanics (HFM), a physics informed deep learning\nframework capable of encoding an important class of physical laws governing\nfluid motions, namely the Navier-Stokes equations. In particular, we seek to\nleverage the underlying conservation laws (i.e., for mass, momentum, and\nenergy) to infer hidden quantities of interest such as velocity and pressure\nfields merely from spatio-temporal visualizations of a passive scaler (e.g.,\ndye or smoke), transported in arbitrarily complex domains (e.g., in human\narteries or brain aneurysms). Our approach towards solving the aforementioned\ndata assimilation problem is unique as we design an algorithm that is agnostic\nto the geometry or the initial and boundary conditions. This makes HFM highly\nflexible in choosing the spatio-temporal domain of interest for data\nacquisition as well as subsequent training and predictions. Consequently, the\npredictions made by HFM are among those cases where a pure machine learning\nstrategy or a mere scientific computing approach simply cannot reproduce. The\nproposed algorithm achieves accurate predictions of the pressure and velocity\nfields in both two and three dimensional flows for several benchmark problems\nmotivated by real-world applications. Our results demonstrate that this\nrelatively simple methodology can be used in physical and biomedical problems\nto extract valuable quantitative information (e.g., lift and drag forces or\nwall shear stresses in arteries) for which direct measurements may not be\npossible.","url_abs":"http://arxiv.org/abs/1808.04327v1","url_pdf":"http://arxiv.org/pdf/1808.04327v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"hidden-fluid-mechanics-a-navier-stokes","repo_url":"https://github.com/maziarraissi/HFM","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"tf","reach":{"status":"unanswered"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1808.04327","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}