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Realizing such devices depends on solving a high\u2010dimensional nonconvex inverse\u2010design problem governed by Maxwell's equations. Adjoint optimization is the standard route to gradients, yet broadband three\u2010dimensional (3D) design typically requires thousands of full\u2010wave forward\/adjoint simulations, making industrial\u2010scale optimization prohibitively slow. To address this bottleneck, a neural adjoint method is introduced, in which a solver\u2010supervised Fourier neural operator (FNO) directly predicts dense, per\u2010voxel 3D adjoint gradient fields from a voxelized permittivity volume. To preserve the sharp, resonance\u2010driven sensitivity peaks that single\u2010pass operator networks tend to oversmooth, a stage\u2010wise FNO is proposed, in which successive stages refine residual errors with progressively higher\u2010frequency emphasis. A domain\u2010specific dataset is curated from paired forward\/adjoint finite\u2010difference time\u2010domain (FDTD) simulations spanning three volumetric tasks: spectral sorting (color routers), achromatic focusing (metalenses), and waveguide mode conversion. Across all benchmarks, the surrogate\u2010driven optimization attains figures of merit within 86%\u201399% of rigorous FDTD\u2010based adjoint optimization whilst reducing end\u2010to\u2010end design time from hours to seconds, with speedups exceeding . These results establish a pathway toward fast large\u2010scale volumetric meta\u2010optical design enabled by neural\u2010operator surrogates.<\/jats:p>","DOI":"10.1002\/nap2.70334","type":"journal-article","created":{"date-parts":[[2026,10,16]],"date-time":"2026-10-16T10:14:25Z","timestamp":1792145665000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Neural Adjoint Inverse Design of Three\u2010Dimensional Nanophotonic Devices"],"prefix":"10.1002","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0009-0006-4592-7629","authenticated-orcid":false,"given":"Chanik","family":"Kang","sequence":"first","affiliation":[{"name":"Department of Artificial Intelligence Hanyang University  Seoul Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0000-5287-3047","authenticated-orcid":false,"given":"Hyewon","family":"Suk","sequence":"additional","affiliation":[{"name":"Department of Artificial Intelligence Semiconductor Engineering Hanyang University  Seoul Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6901-983X","authenticated-orcid":false,"given":"Ikbeom","family":"Jang","sequence":"additional","affiliation":[{"name":"Department of Computer Engineering Hankuk University of Foreign Studies  Yongin Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8959-237X","authenticated-orcid":false,"given":"Haejun","family":"Chung","sequence":"additional","affiliation":[{"name":"Department of Artificial Intelligence Hanyang University  Seoul Korea"},{"name":"Department of Artificial Intelligence Semiconductor Engineering Hanyang University  Seoul Korea"},{"name":"Department of Electronic Engineering Hanyang University  Seoul Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2026,10,16]]},"reference":[{"key":"e_1_2_9_2_1","doi-asserted-by":"publisher","DOI":"10.1038\/s41586\u2010026\u201010369\u2010y"},{"key":"e_1_2_9_3_1","doi-asserted-by":"publisher","DOI":"10.1021\/acsami.4c16216"},{"key":"e_1_2_9_4_1","doi-asserted-by":"publisher","DOI":"10.1021\/acsphotonics.3c00457"},{"key":"e_1_2_9_5_1","doi-asserted-by":"publisher","DOI":"10.1002\/adom.202501769"},{"key":"e_1_2_9_6_1","doi-asserted-by":"publisher","DOI":"10.1002\/adom.202501697"},{"key":"e_1_2_9_7_1","doi-asserted-by":"publisher","DOI":"10.1515\/nanoph\u20102024\u20100269"},{"key":"e_1_2_9_8_1","doi-asserted-by":"publisher","DOI":"10.1038\/s41467\u2010022\u201031019\u20107"},{"key":"e_1_2_9_9_1","doi-asserted-by":"publisher","DOI":"10.1364\/optica.384228"},{"key":"e_1_2_9_10_1","doi-asserted-by":"publisher","DOI":"10.1038\/s41377\u2010025\u201002146\u20109"},{"key":"e_1_2_9_11_1","doi-asserted-by":"publisher","DOI":"10.1021\/acsphotonics.5c02801"},{"key":"e_1_2_9_12_1","doi-asserted-by":"publisher","DOI":"10.1038\/s41566\u2010022\u201001099\u20104"},{"key":"e_1_2_9_13_1","doi-asserted-by":"publisher","DOI":"10.1021\/acsphotonics.2c00876"},{"key":"e_1_2_9_14_1","unstructured":"O. 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