{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T02:08:21Z","timestamp":1778724501444,"version":"3.51.4"},"reference-count":56,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2027,4,12]],"date-time":"2027-04-12T00:00:00Z","timestamp":1807488000000},"content-version":"am","delay-in-days":254,"URL":"http:\/\/www.elsevier.com\/open-access\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"DOI":"10.13039\/100000181","name":"Air Force Office of Scientific Research","doi-asserted-by":"publisher","award":["FA9550-24-1-0327"],"award-info":[{"award-number":["FA9550-24-1-0327"]}],"id":[{"id":"10.13039\/100000181","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Journal of Computational Physics"],"published-print":{"date-parts":[[2026,8]]},"DOI":"10.1016\/j.jcp.2026.114931","type":"journal-article","created":{"date-parts":[[2026,4,8]],"date-time":"2026-04-08T23:08:21Z","timestamp":1775689701000},"page":"114931","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":1,"special_numbering":"C","title":["FEDONet: Fourier-embedded DeepONet for spectrally accurate operator learning"],"prefix":"10.1016","volume":"559","author":[{"given":"Arth","family":"Sojitra","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0009-0007-1188-7937","authenticated-orcid":false,"given":"Mrigank","family":"Dhingra","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2241-4648","authenticated-orcid":false,"given":"Omer","family":"San","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/j.jcp.2026.114931_bib0001","series-title":"Chebyshev and Fourier spectral methods","author":"Boyd","year":"2001"},{"key":"10.1016\/j.jcp.2026.114931_bib0002","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611970425","article-title":"Numerical Analysis of Spectral Methods: Theory and Applications","author":"Gottlieb","year":"1977"},{"key":"10.1016\/j.jcp.2026.114931_bib0003","series-title":"Numerical Recipes: The Art of Scientific Computing","author":"Press","year":"1986"},{"issue":"4","key":"10.1016\/j.jcp.2026.114931_bib0004","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1007\/BF02551274","article-title":"Approximation by superpositions of a sigmoidal function","volume":"2","author":"Cybenko","year":"1989","journal-title":"Math. Contr. Signals Syst."},{"issue":"5","key":"10.1016\/j.jcp.2026.114931_bib0005","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1016\/0893-6080(89)90020-8","article-title":"Multilayer feedforward networks are universal approximators","volume":"2","author":"Hornik","year":"1989","journal-title":"Neural Netw."},{"issue":"9","key":"10.1016\/j.jcp.2026.114931_bib0006","doi-asserted-by":"crossref","first-page":"1481","DOI":"10.1109\/5.58326","article-title":"Networks for approximation and learning","volume":"78","author":"Poggio","year":"1990","journal-title":"Proc. IEEE"},{"issue":"4","key":"10.1016\/j.jcp.2026.114931_bib0007","doi-asserted-by":"crossref","first-page":"911","DOI":"10.1109\/72.392253","article-title":"Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its application to dynamical systems","volume":"6","author":"Chen","year":"1995","journal-title":"IEEE Trans. Neural Netw."},{"issue":"3","key":"10.1016\/j.jcp.2026.114931_bib0008","doi-asserted-by":"crossref","first-page":"561","DOI":"10.1090\/qam\/910462","article-title":"Turbulence and the dynamics of coherent structures. I. Coherent structures","volume":"45","author":"Sirovich","year":"1987","journal-title":"Q Appl. Math."},{"issue":"1","key":"10.1016\/j.jcp.2026.114931_bib0009","doi-asserted-by":"crossref","first-page":"539","DOI":"10.1146\/annurev.fl.25.010193.002543","article-title":"The proper orthogonal decomposition in the analysis of turbulent flows","volume":"25","author":"Berkooz","year":"1993","journal-title":"Annu. Rev. Fluid Mech."},{"key":"10.1016\/j.jcp.2026.114931_bib0010","series-title":"Gaussian Processes for Machine Learning","author":"Rasmussen","year":"2005"},{"issue":"8","key":"10.1016\/j.jcp.2026.114931_bib0011","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1016\/0898-1221(90)90270-T","article-title":"Multiquadrics-A scattered data approximation scheme with applications to computational fluid-dynamics-I surface approximations and partial derivative estimates","volume":"19","author":"Kansa","year":"1990","journal-title":"Comput. Math. Appl."},{"issue":"3","key":"10.1016\/j.jcp.2026.114931_bib0012","first-page":"321","article-title":"Multivariable functional interpolation and adaptive networks","volume":"2","author":"Lowe","year":"1988","journal-title":"Complex Syst."},{"key":"10.1016\/j.jcp.2026.114931_bib0013","doi-asserted-by":"crossref","first-page":"620","DOI":"10.1016\/j.jcp.2019.06.042","article-title":"Data driven governing equations approximation using deep neural networks","volume":"395","author":"Qin","year":"2019","journal-title":"J. Comput. Phys."},{"issue":"3","key":"10.1016\/j.jcp.2026.114931_bib0014","doi-asserted-by":"crossref","first-page":"218","DOI":"10.1038\/s42256-021-00302-5","article-title":"Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators","volume":"3","author":"Lu","year":"2021","journal-title":"Nature Mach. Intell."},{"issue":"1","key":"10.1016\/j.jcp.2026.114931_bib0015","article-title":"Neural operator: learning maps between function spaces with applications to PDEs","volume":"24","author":"Kovachki","year":"2023","journal-title":"J. Mach. Learn. Res."},{"key":"10.1016\/j.jcp.2026.114931_bib0016","unstructured":"Z. Li, N. Kovachki, K. Azizzadenesheli, B. Liu, K. Bhattacharya, A. Stuart, A. Anandkumar, Neural operator: graph kernel network for partial differential equations, 2020a, arXiv: 2003.03485."},{"key":"10.1016\/j.jcp.2026.114931_bib0017","unstructured":"Z. Li, N. Kovachki, K. Azizzadenesheli, B. Liu, K. Bhattacharya, A. Stuart, A. Anandkumar, Multipole graph neural operator for parametric partial differential equations, 2020b, arXiv: 2006.09535."},{"key":"10.1016\/j.jcp.2026.114931_bib0018","unstructured":"Z. Li, N. Kovachki, K. Azizzadenesheli, B. Liu, K. Bhattacharya, A. Stuart, A. Anandkumar, Fourier neural operator for parametric partial differential equations, 2021, arXiv: 2010.08895."},{"key":"10.1016\/j.jcp.2026.114931_bib0019","doi-asserted-by":"crossref","DOI":"10.1016\/j.jcp.2020.109307","article-title":"Data-driven deep learning of partial differential equations in modal space","volume":"408","author":"Wu","year":"2020","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.jcp.2026.114931_bib0020","doi-asserted-by":"crossref","DOI":"10.1016\/j.cma.2022.115783","article-title":"Wavelet neural operator for solving parametric partial differential equations in computational mechanics problems","volume":"404","author":"Tripura","year":"2023","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"10.1016\/j.jcp.2026.114931_bib0021","series-title":"Advances in Neural Information Processing Systems","article-title":"Multiwavelet-based operator learning for differential equations","author":"Gupta","year":"2021"},{"key":"10.1016\/j.jcp.2026.114931_bib0022","series-title":"ICLR 2023 Workshop on Physics for Machine Learning","article-title":"Convolutional neural operators","author":"Raonic","year":"2023"},{"key":"10.1016\/j.jcp.2026.114931_bib0023","unstructured":"J. Kossaifi, N. Kovachki, K. Azizzadenesheli, A. Anandkumar, Multi-grid tensorized fourier neural operator for high-resolution pdes, arXiv preprint arXiv: 2310.00120(2023)."},{"key":"10.1016\/j.jcp.2026.114931_bib0024","unstructured":"Z.-H. Guo, H.-B. Li, MgFNO: multi-grid architecture fourier neural operator for parametric partial differential equations, 2024, arXiv: 2407.08615."},{"issue":"388","key":"10.1016\/j.jcp.2026.114931_bib0025","first-page":"1","article-title":"Fourier neural operator with learned deformations for pdes on general geometries","volume":"24","author":"Li","year":"2023","journal-title":"J. Mach. Learn. Res."},{"key":"10.1016\/j.jcp.2026.114931_bib0026","unstructured":"S. Lanthaler, R. Molinaro, P. Hadorn, S. Mishra, Nonlinear reconstruction for operator learning of pdes with discontinuities, 2022, arXiv: 2210.01074."},{"key":"10.1016\/j.jcp.2026.114931_bib0027","doi-asserted-by":"crossref","unstructured":"Y. Qiu, N. Bridges, P. Chen, Derivative-enhanced Deep Operator Network, 2024, arXiv: 2402.19242.","DOI":"10.52202\/079017-0660"},{"key":"10.1016\/j.jcp.2026.114931_bib0028","doi-asserted-by":"crossref","unstructured":"S.W. Cho, J.Y. Lee, H.J. Hwang, Learning time-dependent PDE via graph neural networks and deep operator network for robust accuracy on irregular grids, 2024, arXiv: 2402.08187.","DOI":"10.2139\/ssrn.5110530"},{"key":"10.1016\/j.jcp.2026.114931_bib0029","unstructured":"S. Li, X. Yu, W. Xing, M. Kirby, A. Narayan, S. Zhe, Multi-resolution active learning of fourier neural operators, 2024, arXiv: 2309.16971."},{"key":"10.1016\/j.jcp.2026.114931_bib0030","doi-asserted-by":"crossref","unstructured":"W.-M. Lei, H.-B. Li, U-WNO: U-net enhanced wavelet neural operator for solving parametric partial differential equations, 2024, arXiv: 2408.08190.","DOI":"10.2139\/ssrn.4932521"},{"key":"10.1016\/j.jcp.2026.114931_bib0031","unstructured":"P. Hu, R. Wang, X. Zheng, T. Zhang, H. Feng, R. Feng, L. Wei, Y. Wang, Z.-M. Ma, T. Wu, Wavelet diffusion neural operator, 2025, arXiv: 2412.04833."},{"key":"10.1016\/j.jcp.2026.114931_bib0032","doi-asserted-by":"crossref","first-page":"422","DOI":"10.1038\/s42254-021-00314-5","article-title":"Physics-informed machine learning","volume":"3","author":"Karniadakis","year":"2021","journal-title":"Nature Rev. Phys."},{"key":"10.1016\/j.jcp.2026.114931_bib0033","unstructured":"S. Wang, Y. Teng, P. Perdikaris, Understanding and mitigating gradient pathologies in physics-informed neural networks, 2020, arXiv: 2001.04536."},{"key":"10.1016\/j.jcp.2026.114931_bib0034","unstructured":"S. Goswami, A. Bora, Y. Yu, G.E. Karniadakis, Physics-informed deep neural operator networks, 2022, arXiv: 2207.05748."},{"key":"10.1016\/j.jcp.2026.114931_bib0035","unstructured":"Z. Li, H. Zheng, N. Kovachki, D. Jin, H. Chen, B. Liu, K. Azizzadenesheli, A. Anandkumar, Physics-informed neural operator for learning partial differential equations, 2023, arXiv: 2111.03794."},{"key":"10.1016\/j.jcp.2026.114931_bib0036","doi-asserted-by":"crossref","unstructured":"M.S. Eshaghi, C. Anitescu, M. Thombre, Y. Wang, X. Zhuang, T. Rabczuk, Variational physics-informed neural operator (VINO) for solving partial differential equations, 2024, arXiv: 2411.06587.","DOI":"10.1016\/j.cma.2025.117785"},{"key":"10.1016\/j.jcp.2026.114931_bib0037","unstructured":"K. Chen, Y. Li, D. Long, W.W. XING, J. Hochhalter, S. Zhe, Pseudo physics-informed neural operators, 2025."},{"key":"10.1016\/j.jcp.2026.114931_bib0038","doi-asserted-by":"crossref","unstructured":"T. Wang, C. Wang, Latent Neural Operator for Solving Forward and Inverse PDE Problems, 2024a, arXiv: 2406.03923.","DOI":"10.52202\/079017-1042"},{"key":"10.1016\/j.jcp.2026.114931_bib0039","unstructured":"T. Wang, C. Wang, Latent neural operator pretraining for solving time-dependent pdes, 2024b, arXiv: 2410.20100."},{"key":"10.1016\/j.jcp.2026.114931_bib0040","unstructured":"Z. Ahmad, S. Chen, M. Yin, A. Kumar, N. Charon, N. Trayanova, M. Maggioni, Diffeomorphic latent neural operators for data-efficient learning of solutions to partial differential equations, 2024, arXiv: 2411.18014."},{"key":"10.1016\/j.jcp.2026.114931_bib0041","unstructured":"D. Long, Z. Xu, Q. Yuan, Y. Yang, S. Zhe, Invertible fourier neural operators for tackling both forward and inverse problems, 2025, arXiv: 2402.11722."},{"key":"10.1016\/j.jcp.2026.114931_bib0042","series-title":"International Conference on Machine Learning","first-page":"12556","article-title":"GNOT: a general neural operator transformer for operator learning","author":"Hao","year":"2023"},{"key":"10.1016\/j.jcp.2026.114931_bib0043","unstructured":"Z. Li, K. Meidani, A.B. Farimani, Transformer for partial differential equations\u2019 operator learning, 2023a, arXiv: 2205.13671."},{"key":"10.1016\/j.jcp.2026.114931_bib0044","first-page":"28010","article-title":"Scalable transformer for pde surrogate modeling","volume":"36","author":"Li","year":"2023","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"10.1016\/j.jcp.2026.114931_bib0045","unstructured":"S.K. Boya, D. Subramani, A physics-informed transformer neural operator for learning generalized solutions of initial boundary value problems, 2025, arXiv: 2412.09009."},{"key":"10.1016\/j.jcp.2026.114931_bib0046","unstructured":"A. Bryutkin, J. Huang, Z. Deng, G. Yang, C.-B. Sch\u00f6nlieb, A. Aviles-Rivero, Hamlet: Graph transformer neural operator for partial differential equations, arXiv preprint arXiv: 2402.03541(2024)."},{"key":"10.1016\/j.jcp.2026.114931_bib0047","first-page":"35836","article-title":"Geometry-informed neural operator for large-scale 3d pdes","volume":"36","author":"Li","year":"2023","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"10.1016\/j.jcp.2026.114931_bib0048","unstructured":"J. Pathak, S. Subramanian, P. Harrington, S. Raja, A. Chattopadhyay, M. Mardani, T. Kurth, D. Hall, Z. Li, K. Azizzadenesheli, et al., Fourcastnet: A global data-driven high-resolution weather model using adaptive fourier neural operators, arXiv preprint arXiv: 2202.11214(2022)."},{"key":"10.1016\/j.jcp.2026.114931_bib0049","first-page":"115001","article-title":"Amortized fourier neural operators","volume":"37","author":"Xiao","year":"2024","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"10.1016\/j.jcp.2026.114931_bib0050","doi-asserted-by":"crossref","DOI":"10.1017\/jfm.2023.331","article-title":"Machine learning building-block-flow wall model for large-eddy simulation","volume":"963","author":"Lozano-Dur\u00e1n","year":"2023","journal-title":"J. Fluid Mech."},{"key":"10.1016\/j.jcp.2026.114931_bib0051","doi-asserted-by":"crossref","DOI":"10.1017\/jfm.2025.10741","article-title":"Compact representation of transonic airfoil buffet flows with observable-augmented machine learning","volume":"1021","author":"Fukami","year":"2025","journal-title":"J. Fluid Mech."},{"key":"10.1016\/j.jcp.2026.114931_bib0052","unstructured":"M. Tancik, P.P. Srinivasan, B. Mildenhall, S. Fridovich-Keil, N. Raghavan, U. Singhal, R. Ramamoorthi, J.T. Barron, R. Ng, Fourier features let networks learn high frequency functions in low dimensional domains, 2020, arXiv: 2006.10739."},{"key":"10.1016\/j.jcp.2026.114931_bib0053","doi-asserted-by":"crossref","DOI":"10.1016\/j.pnucene.2025.105895","article-title":"Surrogate modeling of heat transfer under flow fluctuation conditions using fourier basis-deep operator network with uncertainty quantification","volume":"188","author":"Cheng","year":"2025","journal-title":"Prog. Nucl. Energy"},{"key":"10.1016\/j.jcp.2026.114931_bib0054","unstructured":"N. Rahaman, A. Baratin, D. Arpit, F. Draxler, M. Lin, F.A. Hamprecht, Y. Bengio, A. Courville, On the spectral bias of neural networks, 2019, arXiv: 1806.08734."},{"key":"10.1016\/j.jcp.2026.114931_bib0055","series-title":"Advances in Neural Information Processing Systems","article-title":"Random features for large-scale Kernel machines","volume":"20","author":"Rahimi","year":"2007"},{"issue":"40","key":"10.1016\/j.jcp.2026.114931_bib0056","doi-asserted-by":"crossref","DOI":"10.1126\/sciadv.abi8605","article-title":"Learning the solution operator of parametric partial differential equations with physics-informed DeepONets","volume":"7","author":"Wang","year":"2021","journal-title":"Sci. Adv."}],"container-title":["Journal of Computational Physics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0021999126002846?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0021999126002846?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T01:21:36Z","timestamp":1778721696000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0021999126002846"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,8]]},"references-count":56,"alternative-id":["S0021999126002846"],"URL":"https:\/\/doi.org\/10.1016\/j.jcp.2026.114931","relation":{},"ISSN":["0021-9991"],"issn-type":[{"value":"0021-9991","type":"print"}],"subject":[],"published":{"date-parts":[[2026,8]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"FEDONet: Fourier-embedded DeepONet for spectrally accurate operator learning","name":"articletitle","label":"Article Title"},{"value":"Journal of Computational Physics","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.jcp.2026.114931","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"114931"}}