{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,4]],"date-time":"2026-10-04T03:16:27Z","timestamp":1791083787660,"version":"4.1.0"},"reference-count":33,"publisher":"Oxford University Press (OUP)","issue":"13","license":[{"start":{"date-parts":[[2026,5,15]],"date-time":"2026-05-15T00:00:00Z","timestamp":1778803200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2023YFB4604100"],"award-info":[{"award-number":["2023YFB4604100"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["T2550093"],"award-info":[{"award-number":["T2550093"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12475040"],"award-info":[{"award-number":["12475040"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12320101004"],"award-info":[{"award-number":["12320101004"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004731","name":"Zhejiang Provincial Natural Science Foundation","doi-asserted-by":"publisher","award":["LR26A050001"],"award-info":[{"award-number":["LR26A050001"]}],"id":[{"id":"10.13039\/501100004731","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004731","name":"Zhejiang Provincial Natural Science Foundation","doi-asserted-by":"publisher","award":["LZ24A050002"],"award-info":[{"award-number":["LZ24A050002"]}],"id":[{"id":"10.13039\/501100004731","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,6,24]]},"abstract":"<jats:title>ABSTRACT<\/jats:title>\n                  <jats:p>Thermal diffusion, which governs heat transfer across a wide range of systems\u2014from electronics to industrial processes\u2014is inherently irreversible under the second law of thermodynamics, thus obscuring time-dependent information. To overcome this ill-posedness, this study introduces a physics-informed framework that centers on a novel time-reversal operator learning approach. A finite-difference-based network is first employed to robustly derive heterogeneous material properties. Crucially, the core innovation lies in the operator for thermal retrodiction. Distinct from traditional point-wise solvers, this functional model learns the mapping between function spaces, enabling the direct projection of the final-state thermal field back to its initial state. By synergizing analytical eigenbasis decomposition with frequency-domain operator learning, the time-reversal operator effectively reconstructs the backward propagation of temperature fields. Validated on 3D-printed structures and chips, this operator-driven method achieves retrodiction errors $ \\lt $0.1%, establishing a high-fidelity paradigm for spatiotemporal analysis. This breakthrough has broad implications for non-destructive testing in energy systems, with potential applications extending to a wide class of phenomena such as mass, charge, and light diffusion.<\/jats:p>","DOI":"10.1093\/nsr\/nwag287","type":"journal-article","created":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T12:04:03Z","timestamp":1778760243000},"source":"Crossref","is-referenced-by-count":1,"title":["Learning to reverse thermal diffusion"],"prefix":"10.1093","volume":"13","author":[{"given":"Hanqi","family":"Chen","sequence":"first","affiliation":[{"name":"International Joint Innovation Center, The Electromagnetics Academy, Zhejiang University , Haining 314400 ,","place":["China"]},{"name":"State Key Laboratory of Extreme Photonics and Instrumentation, Zhejiang Key Laboratory of Intelligent Electromagnetic Control and Advanced Electronic Integration, Zhejiang University , Hangzhou 310027 ,","place":["China"]},{"name":"Jinhua Institute of Zhejiang University, Zhejiang 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