{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,20]],"date-time":"2025-11-20T09:12:00Z","timestamp":1763629920074,"version":"3.45.0"},"reference-count":54,"publisher":"IOP Publishing","issue":"4","license":[{"start":{"date-parts":[[2025,11,20]],"date-time":"2025-11-20T00:00:00Z","timestamp":1763596800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2025,11,20]],"date-time":"2025-11-20T00:00:00Z","timestamp":1763596800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/iopscience.iop.org\/info\/page\/text-and-data-mining"}],"funder":[{"name":"National Key Research and Development Program of China","award":["2021YFA0717300"],"award-info":[{"award-number":["2021YFA0717300"]}]}],"content-domain":{"domain":["iopscience.iop.org"],"crossmark-restriction":false},"short-container-title":["Mach. Learn.: Sci. Technol."],"published-print":{"date-parts":[[2025,12,30]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Accurately capturing nonlinear, multiscale plasma dynamics remains a central challenge in plasma physics, typically addressed by incorporating appropriate closures into fluid models. While such models retain certain kinetic fidelity and avoid the high computational cost of full phase-space simulations, designing closures often requires sophisticated, system-specific analysis. Recent advances in machine learning have motivated the use of data-driven approaches to learn fluid closures directly from kinetic simulations. In this study, we introduce a physics-informed Fourier neural operator (PIFNO) that incorporates an implicit fluid closure within the neural network to predict the dynamical evolution of two-dimensional electrostatic plasmas from initial conditions. By incorporating fluid moment equations into its loss function, PIFNO exhibits strong spatial extrapolation capabilities beyond the coverage of the training data. Without prescribing a closure form, the model achieves high accuracy in predicting all physical quantities from fully kinetic simulations of electrostatic turbulence. These results position PIFNO as a promising framework for enabling fast and efficient fluid modeling of complex plasma systems.<\/jats:p>","DOI":"10.1088\/2632-2153\/ae19cd","type":"journal-article","created":{"date-parts":[[2025,10,30]],"date-time":"2025-10-30T22:53:17Z","timestamp":1761864797000},"page":"045050","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Data-driven modeling of electrostatic turbulence by physics-informed Fourier neural operator"],"prefix":"10.1088","volume":"6","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4699-8972","authenticated-orcid":false,"given":"Yuhong","family":"Liu","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1816-1024","authenticated-orcid":true,"given":"Haiyang","family":"Fu","sequence":"additional","affiliation":[]},{"given":"Liang","family":"Wang","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8990-094X","authenticated-orcid":true,"given":"Chuanfei","family":"Dong","sequence":"additional","affiliation":[]},{"given":"Shichen","family":"Wei","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0009-0004-0429-3979","authenticated-orcid":false,"given":"Yitian","family":"Xi","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0009-0008-9783-3928","authenticated-orcid":true,"given":"Chaoshi","family":"Shang","sequence":"additional","affiliation":[]},{"given":"Yilan","family":"Qin","sequence":"additional","affiliation":[]}],"member":"266","published-online":{"date-parts":[[2025,11,20]]},"reference":[{"key":"mlstae19cdbib1","doi-asserted-by":"publisher","first-page":"870","DOI":"10.1016\/j.jcp.2011.02.006","type":"journal-article","volume":"231","author":"T\u00f3th","year":"2012","journal-title":"J. Comput. Phys."},{"key":"mlstae19cdbib2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2020.109510","type":"journal-article","volume":"415","author":"Wang","year":"2020","journal-title":"J. Comput. Phys."},{"key":"mlstae19cdbib3","doi-asserted-by":"publisher","first-page":"11584","DOI":"10.1029\/2019GL083180","type":"journal-article","volume":"46","author":"Dong","year":"2019","journal-title":"Geophys. Res. Lett."},{"key":"mlstae19cdbib4","doi-asserted-by":"publisher","first-page":"2815","DOI":"10.1002\/2017JA024761","type":"journal-article","volume":"123","author":"Wang","year":"2018","journal-title":"J. Geophys. Res."},{"key":"mlstae19cdbib5","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.121.165101","type":"journal-article","volume":"121","author":"Dong","year":"2018","journal-title":"Phys. Rev. Lett."},{"key":"mlstae19cdbib6","doi-asserted-by":"publisher","first-page":"eabn7627","DOI":"10.1126\/sciadv.abn7627","type":"journal-article","volume":"8","author":"Dong","year":"2022","journal-title":"Sci. Adv."},{"key":"mlstae19cdbib7","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevAccelBeams.21.041303","type":"journal-article","volume":"21","author":"Dong","year":"2018","journal-title":"Phys. Rev."},{"key":"mlstae19cdbib8","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevResearch.6.L012016","type":"journal-article","volume":"6","author":"Campbell","year":"2024","journal-title":"Phys. Rev. Res."},{"key":"mlstae19cdbib9","doi-asserted-by":"publisher","DOI":"10.1063\/5.0122087","type":"journal-article","volume":"13","author":"Li","year":"2023","journal-title":"AIP Adv."},{"key":"mlstae19cdbib10","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.98.043207","type":"journal-article","volume":"98","author":"Raymond","year":"2018","journal-title":"Phys. Rev. E"},{"key":"mlstae19cdbib11","doi-asserted-by":"publisher","first-page":"916","DOI":"10.1038\/s41567-020-0919-4","type":"journal-article","volume":"16","author":"Fiuza","year":"2020","journal-title":"Nat. Phys."},{"key":"mlstae19cdbib12","doi-asserted-by":"publisher","first-page":"263","DOI":"10.1038\/s42254-021-00419-x","type":"journal-article","volume":"4","author":"Ji","year":"2022","journal-title":"Nat. Rev. Phys."},{"key":"mlstae19cdbib13","doi-asserted-by":"publisher","first-page":"3019","DOI":"10.1103\/PhysRevLett.64.3019","type":"journal-article","volume":"64","author":"Hammett","year":"1990","journal-title":"Phys. Rev. Lett."},{"key":"mlstae19cdbib14","doi-asserted-by":"publisher","DOI":"10.1017\/S0022377819000850","type":"journal-article","volume":"85","author":"Hunana","year":"2019","journal-title":"J. Plasma Phys."},{"key":"mlstae19cdbib15","doi-asserted-by":"publisher","DOI":"10.1038\/s41598-023-45416-5","type":"journal-article","volume":"13","author":"Burby","year":"2023","journal-title":"Sci. Rep."},{"key":"mlstae19cdbib16","doi-asserted-by":"publisher","first-page":"3199","DOI":"10.1063\/1.1374238","type":"journal-article","volume":"8","author":"Snyder","year":"2001","journal-title":"Phys. Plasmas"},{"key":"mlstae19cdbib17","doi-asserted-by":"publisher","DOI":"10.1063\/5.0012067","type":"journal-article","volume":"27","author":"Ng","year":"2020","journal-title":"Phys. Plasmas"},{"key":"mlstae19cdbib18","doi-asserted-by":"publisher","first-page":"9363","DOI":"10.1029\/2018GL078957","type":"journal-article","volume":"45","author":"Fu","year":"2018","journal-title":"Geophys. Res. Lett."},{"key":"mlstae19cdbib19","doi-asserted-by":"publisher","DOI":"10.1029\/2020GL089747","type":"journal-article","volume":"47","author":"Fu","year":"2020","journal-title":"Geophys. Res. Lett."},{"key":"mlstae19cdbib20","doi-asserted-by":"publisher","first-page":"298","DOI":"10.3934\/fods.2024043","type":"journal-article","volume":"7","author":"Sanderse","year":"2025","journal-title":"Found. Data Sci."},{"key":"mlstae19cdbib21","type":"journal-article","volume":"5","author":"Carvalho","year":"2024","journal-title":"Mach. Learn.: Sci. Technol."},{"key":"mlstae19cdbib22","doi-asserted-by":"publisher","first-page":"21983","DOI":"10.1073\/pnas.1909854116","type":"journal-article","volume":"116","author":"Han","year":"2019","journal-title":"Proc. Natl Acad. Sci."},{"key":"mlstae19cdbib23","doi-asserted-by":"publisher","DOI":"10.1017\/S0022377823000119","type":"journal-article","volume":"89","author":"Donaghy","year":"2023","journal-title":"J. Plasma Phys."},{"key":"mlstae19cdbib24","first-page":"pp 01","type":"conference-proceedings","article-title":"Data-driven modeling of landau damping by fourier neural operator","author":"Wei","year":"2023"},{"key":"mlstae19cdbib25","doi-asserted-by":"publisher","DOI":"10.1029\/2023SW003823","type":"journal-article","volume":"22","author":"Ma","year":"2024","journal-title":"Space Weather"},{"key":"mlstae19cdbib26","doi-asserted-by":"publisher","first-page":"161","DOI":"10.3847\/1538-4357\/adf3ac","type":"journal-article","volume":"990","author":"Shekarpaz","year":"2025","journal-title":"Astrophys. J."},{"key":"mlstae19cdbib27","doi-asserted-by":"publisher","DOI":"10.1063\/1.5129158","type":"journal-article","volume":"27","author":"Ma","year":"2020","journal-title":"Phys. Plasmas"},{"key":"mlstae19cdbib28","doi-asserted-by":"publisher","DOI":"10.1063\/5.0010917","type":"journal-article","volume":"10","author":"Wang","year":"2020","journal-title":"AIP Adv."},{"key":"mlstae19cdbib29","doi-asserted-by":"publisher","DOI":"10.1088\/2632-2153\/acf81a","type":"journal-article","volume":"4","author":"Joglekar","year":"2023","journal-title":"Mach. Learn.: Sci. Technol."},{"key":"mlstae19cdbib30","doi-asserted-by":"publisher","DOI":"10.1016\/j.cpc.2022.108538","type":"journal-article","volume":"282","author":"Cheng","year":"2023","journal-title":"Comput. Phys. Commun."},{"key":"mlstae19cdbib31","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevResearch.4.033192","type":"journal-article","volume":"4","author":"Alves","year":"2022","journal-title":"Phys. Rev. Res."},{"key":"mlstae19cdbib32","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevResearch.5.033079","type":"journal-article","volume":"5","author":"Qin","year":"2023","journal-title":"Phys. Rev. Res."},{"key":"mlstae19cdbib33","doi-asserted-by":"publisher","first-page":"489","DOI":"10.1137\/21M1423956","type":"journal-article","volume":"21","author":"Huang","year":"2023","journal-title":"Multiscale Model. Simul."},{"article-title":"Beyond closure models: Learning chaotic-systems via physics-informed neural operators","year":"2024","author":"Wang","key":"mlstae19cdbib34","type":"conference-proceedings"},{"key":"mlstae19cdbib35","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.2419073122","type":"journal-article","volume":"122","author":"Huang","year":"2025","journal-title":"Proc. Natl Acad. Sci."},{"year":"2021","author":"Kovachki","key":"mlstae19cdbib36","type":"preprint"},{"key":"mlstae19cdbib37","doi-asserted-by":"publisher","first-page":"218","DOI":"10.1038\/s42256-021-00302-5","type":"journal-article","volume":"3","author":"Lu","year":"2021","journal-title":"Nat. Mach. Intell."},{"article-title":"Neural operator: Graph kernel network for partial differential equations","year":"2020","author":"Anandkumar","key":"mlstae19cdbib38","type":"conference-proceedings"},{"key":"mlstae19cdbib39","doi-asserted-by":"publisher","DOI":"10.1088\/2632-2153\/ad8980","type":"journal-article","volume":"5","author":"Quackenbush","year":"2024","journal-title":"Mach. Learn.: Sci. Technol."},{"key":"mlstae19cdbib40","doi-asserted-by":"publisher","DOI":"10.1088\/2632-2153\/acd168","type":"journal-article","volume":"4","author":"Rosofsky","year":"2023","journal-title":"Mach. Learn.: Sci. Technol."},{"key":"mlstae19cdbib41","doi-asserted-by":"publisher","DOI":"10.1088\/2632-2153\/ada0a5","type":"journal-article","volume":"5","author":"Zhao","year":"2024","journal-title":"Mach. Learn.: Sci. Technol."},{"article-title":"Fourier neural operator for parametric partial differential equations","year":"2020","author":"Li","key":"mlstae19cdbib42","type":"conference-proceedings"},{"key":"mlstae19cdbib43","doi-asserted-by":"publisher","DOI":"10.1016\/j.advwatres.2022.104180","type":"journal-article","volume":"163","author":"Wen","year":"2022","journal-title":"Adv. Water Resour."},{"article-title":"Efficient token mixing for transformers via adaptive fourier neural operators","year":"2021","author":"Guibas","key":"mlstae19cdbib44","type":"conference-proceedings"},{"key":"mlstae19cdbib45","first-page":"1","type":"journal-article","volume":"24","author":"Li","year":"2023","journal-title":"J. Mach. Learn. Res."},{"article-title":"Loglo-fno: efficient learning of local and global features in fourier neural operators","year":"2025","author":"Kalimuthu","key":"mlstae19cdbib46","type":"conference-proceedings"},{"key":"mlstae19cdbib47","doi-asserted-by":"publisher","first-page":"36","DOI":"10.1007\/s10894-007-9116-z","type":"journal-article","volume":"27","author":"Hakim","year":"2008","journal-title":"J. Fusion Energy"},{"key":"mlstae19cdbib48","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2022.114778","type":"journal-article","volume":"393","author":"Lu","year":"2022","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"mlstae19cdbib49","doi-asserted-by":"publisher","first-page":"6136","DOI":"10.1038\/s41467-021-26434-1","type":"journal-article","volume":"12","author":"Chen","year":"2021","journal-title":"Nat. Commun."},{"key":"mlstae19cdbib50","doi-asserted-by":"publisher","first-page":"eabq6120","DOI":"10.1126\/sciadv.abq6120","type":"journal-article","volume":"9","author":"Golden","year":"2023","journal-title":"Sci. Adv."},{"key":"mlstae19cdbib51","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2022.111713","type":"journal-article","volume":"473","author":"Lin","year":"2023","journal-title":"J. Comput. Phys."},{"key":"mlstae19cdbib52","doi-asserted-by":"publisher","first-page":"1251","DOI":"10.1007\/s00466-023-02272-4","type":"journal-article","volume":"71","author":"De","year":"2023","journal-title":"Comput. Mech."},{"key":"mlstae19cdbib53","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2021.110768","type":"journal-article","volume":"449","author":"Wang","year":"2022","journal-title":"J. Comput. Phys."},{"key":"mlstae19cdbib54","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2024.116813","type":"journal-article","volume":"421","author":"Wang","year":"2024","journal-title":"Comput. Methods Appl. Mech. Eng."}],"container-title":["Machine Learning: Science and Technology"],"original-title":[],"link":[{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/ae19cd","content-type":"text\/html","content-version":"am","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/ae19cd\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/ae19cd","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/ae19cd\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/ae19cd\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/ae19cd\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/ae19cd\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"similarity-checking"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/ae19cd\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,20]],"date-time":"2025-11-20T09:07:41Z","timestamp":1763629661000},"score":1,"resource":{"primary":{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/ae19cd"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,11,20]]},"references-count":54,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2025,11,20]]},"published-print":{"date-parts":[[2025,12,30]]}},"URL":"https:\/\/doi.org\/10.1088\/2632-2153\/ae19cd","relation":{},"ISSN":["2632-2153"],"issn-type":[{"type":"electronic","value":"2632-2153"}],"subject":[],"published":{"date-parts":[[2025,11,20]]},"assertion":[{"value":"Data-driven modeling of electrostatic turbulence by physics-informed Fourier neural operator","name":"article_title","label":"Article Title"},{"value":"Machine Learning: Science and Technology","name":"journal_title","label":"Journal Title"},{"value":"paper","name":"article_type","label":"Article Type"},{"value":"\u00a9 2025 The Author(s). Published by IOP Publishing Ltd","name":"copyright_information","label":"Copyright Information"},{"value":"2025-06-16","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2025-10-30","name":"date_accepted","label":"Date Accepted","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2025-11-20","name":"date_epub","label":"Online publication date","group":{"name":"publication_dates","label":"Publication dates"}}]}}