{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,12]],"date-time":"2025-03-12T04:28:06Z","timestamp":1741753686087,"version":"3.38.0"},"reference-count":44,"publisher":"IOP Publishing","issue":"1","license":[{"start":{"date-parts":[[2025,3,11]],"date-time":"2025-03-11T00:00:00Z","timestamp":1741651200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2025,3,11]],"date-time":"2025-03-11T00:00:00Z","timestamp":1741651200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/iopscience.iop.org\/info\/page\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100002347","name":"Bundesministerium f\u00fcr Bildung und Forschung","doi-asserted-by":"crossref","award":["16ME0679K"],"award-info":[{"award-number":["16ME0679K"]}],"id":[{"id":"10.13039\/501100002347","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["iopscience.iop.org"],"crossmark-restriction":false},"short-container-title":["Mach. Learn.: Sci. Technol."],"published-print":{"date-parts":[[2025,3,31]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Correctly capturing the transition to turbulence in a barotropic instability requires fine spatial resolution. To reduce computational cost, we propose a dynamic super-resolution approach where a transient simulation on a coarse mesh is frequently corrected using a U-net-type neural network. For the nonlinear shallow water equations, we demonstrate that a simulation with the Icosahedral Nonhydrostatic ocean model with a 20\u2009km resolution plus dynamic super-resolution trained on a 2.5km resolution achieves discretization errors comparable to a simulation with 10\u2009km resolution. The neural network, originally developed for image-based super-resolution in post-processing, is trained to compute the difference between solutions on both meshes and is used to correct the coarse mesh solution every 12\u2009h. We show that the ML-corrected coarse solution correctly maintains a balanced flow and captures the transition to turbulence in line with the higher resolution simulation. After an 8\u2009d simulation, the <jats:italic>L<\/jats:italic>\n                  <jats:sub>2<\/jats:sub>-error of the corrected run is similar to a simulation run on a finer mesh. While mass is conserved in the corrected runs, we observe some spurious generation of kinetic energy.<\/jats:p>","DOI":"10.1088\/2632-2153\/ada19f","type":"journal-article","created":{"date-parts":[[2024,12,19]],"date-time":"2024-12-19T22:56:02Z","timestamp":1734648962000},"page":"015060","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Dynamic deep learning based super-resolution for the shallow water equations"],"prefix":"10.1088","volume":"6","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2923-8907","authenticated-orcid":true,"given":"Maximilian","family":"Witte","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2444-3861","authenticated-orcid":true,"given":"Fabr\u00edcio R","family":"Lapolli","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9838-6321","authenticated-orcid":true,"given":"Philip","family":"Freese","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0287-2120","authenticated-orcid":true,"given":"Sebastian","family":"G\u00f6tschel","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1904-2473","authenticated-orcid":true,"given":"Daniel","family":"Ruprecht","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7525-5732","authenticated-orcid":false,"given":"Peter","family":"Korn","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6537-3690","authenticated-orcid":false,"given":"Christopher","family":"Kadow","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"266","published-online":{"date-parts":[[2025,3,11]]},"reference":[{"article-title":"Checkerboard artifact free sub-pixel convolution: a note on sub-pixel convolution, resize convolution and convolution resize","year":"2017","author":"Aitken","key":"mlstada19fbib1"},{"key":"mlstada19fbib2","doi-asserted-by":"publisher","first-page":"661","DOI":"10.1007\/s10236-022-01523-x","article-title":"Super-resolution data assimilation","volume":"72","author":"Barth\u00e9l\u00e9my","year":"2022","journal-title":"Ocean Dyn."},{"key":"mlstada19fbib3","doi-asserted-by":"publisher","DOI":"10.1029\/2021MS002794","article-title":"Correcting coarse-grid weather and climate models by machine learning from global storm-resolving simulations","volume":"14","author":"Bretherton","year":"2022","journal-title":"J. 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