{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,23]],"date-time":"2026-04-23T10:08:52Z","timestamp":1776938932368,"version":"3.51.4"},"reference-count":61,"publisher":"IOP Publishing","issue":"1","license":[{"start":{"date-parts":[[2023,2,9]],"date-time":"2023-02-09T00:00:00Z","timestamp":1675900800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2023,2,9]],"date-time":"2023-02-09T00:00:00Z","timestamp":1675900800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/iopscience.iop.org\/info\/page\/text-and-data-mining"}],"funder":[{"name":"Oracle"},{"name":"Safe and Ef\ufb01cient Transportation University Transportation Center"},{"name":"National University Transportation Center"},{"name":"National Science Foundation Graduate Research Fellowship","award":["DGE 1745016"],"award-info":[{"award-number":["DGE 1745016"]}]},{"DOI":"10.13039\/100000140","name":"United States Department of Transportation","doi-asserted-by":"crossref","id":[{"id":"10.13039\/100000140","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/100000015","name":"U.S. Department of Energy","doi-asserted-by":"crossref","id":[{"id":"10.13039\/100000015","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":[[2023,3,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Data-driven turbulence modeling is experiencing a surge in interest following algorithmic and hardware developments in the data sciences. We discuss an approach using the differentiable physics paradigm that combines known physics with machine learning to develop closure models for Burgers\u2019 turbulence. We consider the one-dimensional Burgers system as a prototypical test problem for modeling the unresolved terms in advection-dominated turbulence problems. We train a series of models that incorporate varying degrees of physical assumptions on an <jats:italic>a posteriori<\/jats:italic> loss function to test the efficacy of models across a range of system parameters, including viscosity, time, and grid resolution. We find that constraining models with inductive biases in the form of partial differential equations that contain known physics or existing closure approaches produces highly data-efficient, accurate, and generalizable models, outperforming state-of-the-art baselines. Addition of structure in the form of physics information also brings a level of interpretability to the models, potentially offering a stepping stone to the future of closure modeling.<\/jats:p>","DOI":"10.1088\/2632-2153\/acb19c","type":"journal-article","created":{"date-parts":[[2023,1,9]],"date-time":"2023-01-09T22:37:56Z","timestamp":1673303876000},"page":"015017","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":7,"title":["Differentiable physics-enabled closure modeling for Burgers\u2019 turbulence"],"prefix":"10.1088","volume":"4","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0332-8840","authenticated-orcid":true,"given":"Varun","family":"Shankar","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2724-6591","authenticated-orcid":false,"given":"Vedant","family":"Puri","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8516-5485","authenticated-orcid":false,"given":"Ramesh","family":"Balakrishnan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9731-8936","authenticated-orcid":true,"given":"Romit","family":"Maulik","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1060-5495","authenticated-orcid":false,"given":"Venkatasubramanian","family":"Viswanathan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"266","published-online":{"date-parts":[[2023,2,9]]},"reference":[{"key":"mlstacb19cbib1","volume":"vol 9","author":"Deville","year":"2002"},{"key":"mlstacb19cbib2","doi-asserted-by":"publisher","first-page":"343","DOI":"10.1016\/S0169-5983(99)00004-0","article-title":"Simulating turbulence in complex geometries","volume":"24","author":"Karniadakis","year":"1999","journal-title":"Fluid Dyn. 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