{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,21]],"date-time":"2026-06-21T07:47:53Z","timestamp":1782028073898,"version":"3.54.5"},"reference-count":34,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T00:00:00Z","timestamp":1777334400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T00:00:00Z","timestamp":1777334400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Engineering with Computers"],"published-print":{"date-parts":[[2026,6]]},"DOI":"10.1007\/s00366-026-02321-5","type":"journal-article","created":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T19:50:31Z","timestamp":1777405831000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["GN-UNet: physics-informed temperature field prediction with gradient-guided attention"],"prefix":"10.1007","volume":"42","author":[{"given":"Fangyuan","family":"Sun","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shuai","family":"Yan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xufeng","family":"Huang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qi","family":"Zhou","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jiexiang","family":"Hu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,4,28]]},"reference":[{"issue":"1","key":"2321_CR1","doi-asserted-by":"publisher","first-page":"256","DOI":"10.1109\/JESTPE.2019.2953102","volume":"8","author":"AC Iradukunda","year":"2020","unstructured":"Iradukunda AC, Huitink DR, Luo F (2020) A review of advanced thermal management solutions and the implications for integration in high-voltage packages. IEEE J Emerg Sel Top Power Electron 8(1):256\u2013271","journal-title":"IEEE J Emerg Sel Top Power Electron"},{"key":"2321_CR2","doi-asserted-by":"publisher","DOI":"10.1016\/j.knosys.2021.107151","volume":"227","author":"Q Lin","year":"2021","unstructured":"Lin Q, Hu J, Zhou Q et al (2021) Multi-output Gaussian process prediction for computationally expensive problems with multiple levels of fidelity. Knowl-Based Syst 227:107151","journal-title":"Knowl-Based Syst"},{"issue":"4","key":"2321_CR3","doi-asserted-by":"publisher","first-page":"1885","DOI":"10.1007\/s00158-020-02583-7","volume":"62","author":"Q Zhou","year":"2020","unstructured":"Zhou Q, Wu Y, Guo Z et al (2020) A generalized hierarchical co-Kriging model for multi-fidelity data fusion. Struct Multidiscip Optim 62(4):1885\u20131904","journal-title":"Struct Multidiscip Optim"},{"issue":"4","key":"2321_CR4","doi-asserted-by":"publisher","first-page":"18","DOI":"10.1109\/5254.708428","volume":"13","author":"MA Hearst","year":"1998","unstructured":"Hearst MA, Dumais ST, Osuna E et al (1998) Support vector machines. IEEE Intell Syst Appl 13(4):18\u201328","journal-title":"IEEE Intell Syst Appl"},{"key":"2321_CR5","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2023.126267","volume":"545","author":"X Kang","year":"2023","unstructured":"Kang X, Guo J, Song B et al (2023) Interpretability for reliable, efficient, and self-cognitive DNNs: from theories to applications. Neurocomputing 545:126267","journal-title":"Neurocomputing"},{"issue":"6","key":"2321_CR6","doi-asserted-by":"publisher","first-page":"3127","DOI":"10.1007\/s00158-020-02659-4","volume":"62","author":"X Chen","year":"2020","unstructured":"Chen X, Chen X, Zhou W et al (2020) The heat source layout optimization using deep learning surrogate modeling. Struct Multidiscip Optim 62(6):3127\u20133148","journal-title":"Struct Multidiscip Optim"},{"issue":"11","key":"2321_CR7","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s11433-021-1755-6","volume":"64","author":"X Chen","year":"2021","unstructured":"Chen X, Zhao X, Gong Z et al (2021) A deep neural network surrogate modeling benchmark for temperature field prediction of heat source layout. Sci China Phys, Mech Astron 64(11):1","journal-title":"Sci China Phys, Mech Astron"},{"issue":"4","key":"2321_CR8","doi-asserted-by":"publisher","first-page":"2287","DOI":"10.1007\/s00158-021-02983-3","volume":"64","author":"X Zhao","year":"2021","unstructured":"Zhao X, Gong Z, Zhang J et al (2021) A surrogate model with data augmentation and deep transfer learning for temperature field prediction of heat source layout. Struct Multidiscip Optim 64(4):2287\u20132306","journal-title":"Struct Multidiscip Optim"},{"key":"2321_CR9","doi-asserted-by":"publisher","DOI":"10.1016\/j.engappai.2022.105516","volume":"117","author":"X Zhao","year":"2023","unstructured":"Zhao X, Gong Z, Zhang Y et al (2023) Physics-informed convolutional neural networks for temperature field prediction of heat source layout without labeled data. Eng Appl Artif Intell 117:105516","journal-title":"Eng Appl Artif Intell"},{"key":"2321_CR10","doi-asserted-by":"publisher","DOI":"10.1016\/j.applthermaleng.2023.121499","volume":"236","author":"C Wang","year":"2024","unstructured":"Wang C, Vafai K (2024) Heat transfer enhancement for 3D chip thermal simulation and prediction. Appl Therm Eng 236:121499","journal-title":"Appl Therm Eng"},{"key":"2321_CR11","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijthermalsci.2025.109738","volume":"212","author":"Y She","year":"2025","unstructured":"She Y, Hu Z, Qi H et al (2025) 3D temperature field reconstruction for automotive forging dies based on heterogeneous triocular vision. Int J Therm Sci 212:109738","journal-title":"Int J Therm Sci"},{"key":"2321_CR12","doi-asserted-by":"publisher","DOI":"10.1016\/j.icheatmasstransfer.2024.108330","volume":"159","author":"M Gholampour","year":"2024","unstructured":"Gholampour M, Hashemi Z, Wu MC et al (2024) Parameterized physics-informed neural networks for a transient thermal problem: a pure physics-driven approach. Int Commun Heat Mass Transfer 159:108330","journal-title":"Int Commun Heat Mass Transfer"},{"key":"2321_CR13","unstructured":"Dosovitskiy A, Beyer L, Kolesnikov A et al (2020). An image is worth 16x16 words: transformers for image recognition at scale. abs\/2010.11929."},{"key":"2321_CR14","doi-asserted-by":"crossref","unstructured":"Liu Z, Lin Y, Cao Y, et al (2021). Swin transformer: hierarchical vision transformer using shifted windows. In: Proceedings of the 2021 IEEE\/CVF international conference on computer vision (ICCV), pp. 10\u201317","DOI":"10.1109\/ICCV48922.2021.00986"},{"key":"2321_CR15","doi-asserted-by":"crossref","unstructured":"Dong X, Bao J, Chen D, et al (2021). CSWin transformer: a general vision transformer backbone with cross-shaped windows.","DOI":"10.1109\/CVPR52688.2022.01181"},{"key":"2321_CR16","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2024.117109","volume":"428","author":"O Ovadia","year":"2024","unstructured":"Ovadia O, Kahana A, Stinis P et al (2024) ViTO: vision transformer-operator. Comput Methods Appl Mech Eng 428:117109","journal-title":"Comput Methods Appl Mech Eng"},{"key":"2321_CR17","doi-asserted-by":"publisher","DOI":"10.1016\/j.engappai.2023.106893","volume":"126","author":"X Pan","year":"2023","unstructured":"Pan X, Tang J, Xia H et al (2023) Combustion state identification of MSWI processes using ViT-IDFC. Eng Appl Artif Intell 126:106893","journal-title":"Eng Appl Artif Intell"},{"key":"2321_CR18","doi-asserted-by":"publisher","DOI":"10.1016\/j.engappai.2024.108859","volume":"136","author":"Z Sun","year":"2024","unstructured":"Sun Z, Zhang J, Chen Z et al (2024) Image super-resolution reconstruction using swin transformer with efficient channel attention networks. Eng Appl Artif Intell 136:108859","journal-title":"Eng Appl Artif Intell"},{"key":"2321_CR19","doi-asserted-by":"publisher","DOI":"10.1016\/j.applthermaleng.2024.125033","volume":"260","author":"Z Hu","year":"2025","unstructured":"Hu Z, Wang Y, Qi H et al (2025) Real-time 3D temperature field reconstruction for aluminum alloy forging die using swin transformer integrated deep learning framework. Appl Therm Eng 260:125033","journal-title":"Appl Therm Eng"},{"key":"2321_CR20","doi-asserted-by":"crossref","unstructured":"Hassani A, Walton S, Li J et al (2023). Neighborhood attention transformer. In: Proceedings of the 2023 IEEE\/CVF conference on computer vision and pattern recognition (CVPR), pp. 17\u201324","DOI":"10.1109\/CVPR52729.2023.00599"},{"key":"2321_CR21","doi-asserted-by":"crossref","unstructured":"Xia Z, Pan X, Song S, et al (2022). Vision transformer with deformable attention. In: Proceedings of the 2022 IEEE\/CVF conference on computer vision and pattern recognition (CVPR), pp. 18\u201324","DOI":"10.1109\/CVPR52688.2022.00475"},{"key":"2321_CR22","doi-asserted-by":"publisher","first-page":"1227","DOI":"10.1016\/j.ijheatmasstransfer.2016.05.122","volume":"101","author":"J-B Bouquet","year":"2016","unstructured":"Bouquet J-B, Burgaud F, Rimoli JJ (2016) Exploiting length-dependent effects for the design of single-material systems with enhanced thermal transport properties. Int J Heat Mass Transfer 101:1227\u20131236","journal-title":"Int J Heat Mass Transfer"},{"key":"2321_CR23","doi-asserted-by":"publisher","first-page":"210","DOI":"10.1016\/j.ijheatmasstransfer.2016.12.007","volume":"108","author":"K Chen","year":"2017","unstructured":"Chen K, Xing J, Wang S et al (2017) Heat source layout optimization in two-dimensional heat conduction using simulated annealing method. Int J Heat Mass Transf 108:210\u2013219","journal-title":"Int J Heat Mass Transf"},{"key":"2321_CR24","doi-asserted-by":"publisher","first-page":"432","DOI":"10.1016\/j.ijheatmasstransfer.2018.02.001","volume":"122","author":"Y Aslan","year":"2018","unstructured":"Aslan Y, Puskely J, Yarovoy A (2018) Heat source layout optimization for two-dimensional heat conduction using iterative reweighted L1-norm convex minimization. Int J Heat Mass Transfer 122:432\u2013441","journal-title":"Int J Heat Mass Transfer"},{"issue":"4","key":"2321_CR25","doi-asserted-by":"publisher","first-page":"799","DOI":"10.1016\/0017-9310(96)00175-5","volume":"40","author":"A Bejan","year":"1997","unstructured":"Bejan A (1997) Constructal-theory network of conducting paths for cooling a heat generating volume. Int J Heat Mass Transfer 40(4):799\u2013816","journal-title":"Int J Heat Mass Transfer"},{"key":"2321_CR26","unstructured":"Vaswani A, Shazeer NM, Parmar N et al (2017). Attention is all you need. In: Proceedings of the neural information processing systems"},{"key":"2321_CR27","doi-asserted-by":"crossref","unstructured":"Ronneberger O, Fischer P, Brox T (2015). U-Net: convolutional networks for biomedical image segmentation. In: Proceedings of the medical image computing and computer-assisted intervention \u2013 MICCAI 2015, Springer International Publishing, Cham.","DOI":"10.1007\/978-3-319-24574-4_28"},{"key":"2321_CR28","unstructured":"Cao H, Wang Y, Chen J, et al (2021). Swin-Unet: Unet-like pure transformer for medical image segmentation. In: proceedings of the ECCV workshops"},{"key":"2321_CR29","doi-asserted-by":"publisher","DOI":"10.1016\/j.inffus.2024.102634","volume":"113","author":"X Liu","year":"2025","unstructured":"Liu X, Gao P, Yu T et al (2025) CSWin-UNet: transformer UNet with cross-shaped windows for medical image segmentation. Inf Fusion 113:102634","journal-title":"Inf Fusion"},{"key":"2321_CR30","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2025.118348","volume":"447","author":"T Yang","year":"2025","unstructured":"Yang T, Qian Z, Hang N et al (2025) S-PINN: stabilized physics-informed neural networks for alleviating barriers between multi-level co-optimization. Comput Methods Appl Mech Eng 447:118348","journal-title":"Comput Methods Appl Mech Eng"},{"key":"2321_CR31","doi-asserted-by":"crossref","unstructured":"Holzschuh BJ, Vegetti S, Thuerey N (2023). Solving inverse physics problems with score matching. In: Proceedings of the neural information processing systems","DOI":"10.52202\/075280-2706"},{"key":"2321_CR32","doi-asserted-by":"publisher","DOI":"10.1016\/j.icheatmasstransfer.2025.109098","volume":"166","author":"MC Ignuta-Ciuncanu","year":"2025","unstructured":"Ignuta-Ciuncanu MC, ST\u00e4RK H, Martinez-Botas RF (2025) Evolutionary design of conductive pathways using a generative autoencoder. Int Commun Heat Mass Transfer 166:109098","journal-title":"Int Commun Heat Mass Transfer"},{"key":"2321_CR33","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijheatmasstransfer.2023.124205","volume":"211","author":"X Chen","year":"2023","unstructured":"Chen X, Yao W, Zhou W et al (2023) A general differentiable layout optimization framework for heat transfer problems. Int J Heat Mass Transfer 211:124205","journal-title":"Int J Heat Mass Transfer"},{"key":"2321_CR34","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijheatmasstransfer.2021.122263","volume":"184","author":"D Otaki","year":"2022","unstructured":"Otaki D, Nonaka H, Yamada N (2022) Thermal design optimization of electronic circuit board layout with transient heating chips by using Bayesian optimization and thermal network model. Int J Heat Mass Transfer 184:122263","journal-title":"Int J Heat Mass Transfer"}],"container-title":["Engineering with Computers"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00366-026-02321-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00366-026-02321-5","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00366-026-02321-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,6,21]],"date-time":"2026-06-21T07:06:39Z","timestamp":1782025599000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00366-026-02321-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,4,28]]},"references-count":34,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2026,6]]}},"alternative-id":["2321"],"URL":"https:\/\/doi.org\/10.1007\/s00366-026-02321-5","relation":{},"ISSN":["0177-0667","1435-5663"],"issn-type":[{"value":"0177-0667","type":"print"},{"value":"1435-5663","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,4,28]]},"assertion":[{"value":"10 November 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 April 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 April 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"83"}}