{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,4]],"date-time":"2026-07-04T15:17:12Z","timestamp":1783178232236,"version":"3.54.6"},"reference-count":40,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"DOI":"10.13039\/501100012234","name":"Shenzhen Peacock Plan","doi-asserted-by":"publisher","award":["KQTD20200820113110016"],"award-info":[{"award-number":["KQTD20200820113110016"]}],"id":[{"id":"10.13039\/501100012234","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["524705095"],"award-info":[{"award-number":["524705095"]}],"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":["12472117"],"award-info":[{"award-number":["12472117"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100021171","name":"Basic and Applied Basic Research Foundation of Guangdong Province","doi-asserted-by":"publisher","award":["2023B1515120014"],"award-info":[{"award-number":["2023B1515120014"]}],"id":[{"id":"10.13039\/501100021171","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Engineering Applications of Artificial Intelligence"],"published-print":{"date-parts":[[2026,10]]},"DOI":"10.1016\/j.engappai.2026.115265","type":"journal-article","created":{"date-parts":[[2026,6,5]],"date-time":"2026-06-05T16:23:05Z","timestamp":1780676585000},"page":"115265","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"P1","title":["Gaussian kernel Deep Operator Network for dynamic response prediction on variable three-dimensional geometries"],"prefix":"10.1016","volume":"181","author":[{"ORCID":"https:\/\/orcid.org\/0009-0004-6808-6645","authenticated-orcid":false,"given":"Chi","family":"Zhang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhijun","family":"Yang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Guangya","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hao","family":"Chen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2531-5968","authenticated-orcid":false,"given":"Guanxin","family":"Huang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Guangyao","family":"Li","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hu","family":"Wang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"key":"10.1016\/j.engappai.2026.115265_b1","series-title":"Physics-informed DeepONet with stiffness-based loss functions for structural response prediction","author":"Ahmed","year":"2024"},{"issue":"2","key":"10.1016\/j.engappai.2026.115265_b2","doi-asserted-by":"crossref","first-page":"525","DOI":"10.1007\/s00466-019-01740-0","article-title":"Prediction of aerodynamic flow fields using convolutional neural networks","volume":"64","author":"Bhatnagar","year":"2019","journal-title":"Comput. Mech."},{"issue":"1","key":"10.1016\/j.engappai.2026.115265_b3","doi-asserted-by":"crossref","DOI":"10.1177\/1687814016628396","article-title":"Compressor performance prediction using a novel feed-forward neural network based on Gaussian kernel function","volume":"8","author":"Fei","year":"2016","journal-title":"Adv. Mech. Eng."},{"issue":"12","key":"10.1016\/j.engappai.2026.115265_b4","doi-asserted-by":"crossref","DOI":"10.1063\/5.0170101","article-title":"Deep learning-based surrogate models for parametrized PDEs: Handling geometric variability through graph neural networks","volume":"33","author":"Franco","year":"2023","journal-title":"Chaos: An Interdiscip. J. Nonlinear Sci."},{"key":"10.1016\/j.engappai.2026.115265_b5","doi-asserted-by":"crossref","DOI":"10.1016\/j.cma.2022.114587","article-title":"A physics-informed variational DeepONet for predicting crack path in quasi-brittle materials","volume":"391","author":"Goswami","year":"2022","journal-title":"Comput. Methods Appl. Mech. Engrg."},{"key":"10.1016\/j.engappai.2026.115265_b6","doi-asserted-by":"crossref","unstructured":"Guo, X., Li, W., Iorio, F., 2016. Convolutional neural networks for steady flow approximation. In: Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. pp. 481\u2013490.","DOI":"10.1145\/2939672.2939738"},{"key":"10.1016\/j.engappai.2026.115265_b7","doi-asserted-by":"crossref","DOI":"10.1016\/j.cma.2023.116681","article-title":"En-DeepONet: An enrichment approach for enhancing the expressivity of neural operators with applications to seismology","volume":"420","author":"Haghighat","year":"2024","journal-title":"Comput. Methods Appl. Mech. Engrg."},{"key":"10.1016\/j.engappai.2026.115265_b8","doi-asserted-by":"crossref","DOI":"10.1016\/j.cma.2024.117130","article-title":"Geom-deeponet: A point-cloud-based deep operator network for field predictions on 3d parameterized geometries","volume":"429","author":"He","year":"2024","journal-title":"Comput. Methods Appl. Mech. Engrg."},{"key":"10.1016\/j.engappai.2026.115265_b9","doi-asserted-by":"crossref","DOI":"10.1016\/j.cma.2023.116277","article-title":"Novel DeepONet architecture to predict stresses in elastoplastic structures with variable complex geometries and loads","volume":"415","author":"He","year":"2023","journal-title":"Comput. Methods Appl. Mech. Engrg."},{"issue":"8","key":"10.1016\/j.engappai.2026.115265_b10","doi-asserted-by":"crossref","first-page":"5257","DOI":"10.1007\/s00707-024-03991-2","article-title":"Predictions of transient vector solution fields with sequential deep operator network","volume":"235","author":"He","year":"2024","journal-title":"Acta Mech."},{"key":"10.1016\/j.engappai.2026.115265_b11","doi-asserted-by":"crossref","DOI":"10.1016\/j.engappai.2023.107258","article-title":"Sequential deep operator networks (s-deeponet) for predicting full-field solutions under time-dependent loads","volume":"127","author":"He","year":"2024","journal-title":"Eng. Appl. Artif. Intell."},{"issue":"2","key":"10.1016\/j.engappai.2026.115265_b12","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1016\/S0045-7949(00)00127-9","article-title":"Structural optimization under equivalent static loads transformed from dynamic loads based on displacement","volume":"79","author":"Kang","year":"2001","journal-title":"Comput. Struct."},{"key":"10.1016\/j.engappai.2026.115265_b13","series-title":"Physics-informed DeepONet coupled with FEM for convective transport in porous media with sharp Gaussian sources","author":"Kara","year":"2025"},{"issue":"6","key":"10.1016\/j.engappai.2026.115265_b14","first-page":"90","article-title":"Review on determining number of cluster in K-means clustering","volume":"1","author":"Kodinariya","year":"2013","journal-title":"Int. J."},{"key":"10.1016\/j.engappai.2026.115265_b15","doi-asserted-by":"crossref","DOI":"10.1016\/j.ijheatmasstransfer.2022.123809","article-title":"Data-driven and physics-informed deep learning operators for solution of heat conduction equation with parametric heat source","volume":"203","author":"Koric","year":"2023","journal-title":"Int. J. Heat Mass Transfer"},{"key":"10.1016\/j.engappai.2026.115265_b16","series-title":"Deep neural networks as gaussian processes","author":"Lee","year":"2017"},{"issue":"2","key":"10.1016\/j.engappai.2026.115265_b17","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1016\/S0031-3203(02)00060-2","article-title":"The global k-means clustering algorithm","volume":"36","author":"Likas","year":"2003","journal-title":"Pattern Recognit."},{"issue":"1","key":"10.1016\/j.engappai.2026.115265_b18","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1016\/j.tws.2010.10.003","article-title":"Effects of wall thickness and geometric shape on thin-walled parts structural performance","volume":"49","author":"Liu","year":"2011","journal-title":"Thin-Walled Struct."},{"key":"10.1016\/j.engappai.2026.115265_b19","series-title":"Deeponet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators","author":"Lu","year":"2019"},{"issue":"3","key":"10.1016\/j.engappai.2026.115265_b20","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":"Nat. Mach. Intell."},{"issue":"5","key":"10.1016\/j.engappai.2026.115265_b21","doi-asserted-by":"crossref","first-page":"1207","DOI":"10.1007\/s12239-020-0114-8","article-title":"Analytical sensitivity analysis method of cross-sectional shape for thin-walled automobile frame considering global performances","volume":"21","author":"Ma","year":"2020","journal-title":"Int. J. Automot. Technol."},{"key":"10.1016\/j.engappai.2026.115265_b22","series-title":"A kernel-based approach for modelling Gaussian processes with functional information","author":"Nicholson","year":"2022"},{"key":"10.1016\/j.engappai.2026.115265_b23","series-title":"2019 9th Annual Information Technology, Electromechanical Engineering and Microelectronics Conference (Iemecon)","first-page":"279","article-title":"The impact of data pre-processing techniques and dimensionality reduction on the accuracy of machine learning","author":"Obaid","year":"2019"},{"issue":"3","key":"10.1016\/j.engappai.2026.115265_b24","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1007\/s00158-010-0530-x","article-title":"Technical overview of the equivalent static loads method for non-linear static response structural optimization","volume":"43","author":"Park","year":"2011","journal-title":"Struct. Multidiscip. Optim."},{"key":"10.1016\/j.engappai.2026.115265_b25","doi-asserted-by":"crossref","unstructured":"Park, J.J., Florence, P., Straub, J., Newcombe, R., Lovegrove, S., 2019. Deepsdf: Learning continuous signed distance functions for shape representation. In: Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition. pp. 165\u2013174.","DOI":"10.1109\/CVPR.2019.00025"},{"issue":"6","key":"10.1016\/j.engappai.2026.115265_b26","doi-asserted-by":"crossref","first-page":"541","DOI":"10.1002\/cyto.a.20258","article-title":"A new \u201clogicle\u201d display method avoids deceptive effects of logarithmic scaling for low signals and compensated data","volume":"69","author":"Parks","year":"2006","journal-title":"Cytom. Part A: J. Int. Soc. Anal. Cytol."},{"issue":"4","key":"10.1016\/j.engappai.2026.115265_b27","doi-asserted-by":"crossref","first-page":"2133","DOI":"10.3390\/vehicles6040104","article-title":"Investigation of the impact of a vehicle front hood striker geometry on static stiffness performance","volume":"6","author":"Pinzaru","year":"2024","journal-title":"Vehicles"},{"key":"10.1016\/j.engappai.2026.115265_b28","first-page":"1","article-title":"Development of car hood for stiffness improvement using FEA system","volume":"3","author":"Rodke","year":"2015","journal-title":"Int. J. Sci. Res. Dev"},{"key":"10.1016\/j.engappai.2026.115265_b29","series-title":"Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond","author":"Scholkopf","year":"2018"},{"issue":"6","key":"10.1016\/j.engappai.2026.115265_b30","first-page":"2301","article-title":"Gnn-surrogate: A hierarchical and adaptive graph neural network for parameter space exploration of unstructured-mesh ocean simulations","volume":"28","author":"Shi","year":"2022","journal-title":"IEEE Trans. Vis. Comput. Graphics"},{"issue":"7","key":"10.1016\/j.engappai.2026.115265_b31","doi-asserted-by":"crossref","first-page":"841","DOI":"10.1111\/mice.13312","article-title":"Multifidelity graph neural networks for efficient and accurate mesh-based partial differential equations surrogate modeling","volume":"40","author":"Taghizadeh","year":"2025","journal-title":"Computer-Aided Civ. Infrastruct. Eng."},{"key":"10.1016\/j.engappai.2026.115265_b32","series-title":"Enhanced deeponet for modeling partial differential operators considering multiple input functions","author":"Tan","year":"2022"},{"issue":"1","key":"10.1016\/j.engappai.2026.115265_b33","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1177\/1045389X19880016","article-title":"Toward lightweight smart automotive hood structures for head impact mitigation: Integration of active stiffness control composites","volume":"31","author":"Vyas","year":"2020","journal-title":"J. Intell. Mater. Syst. Struct."},{"key":"10.1016\/j.engappai.2026.115265_b34","doi-asserted-by":"crossref","DOI":"10.1016\/j.cma.2025.117750","article-title":"Phase-field hydraulic fracturing operator network based on en-DeepONet with integrated physics-informed mechanisms","volume":"437","author":"Wang","year":"2025","journal-title":"Comput. Methods Appl. Mech. Engrg."},{"issue":"1","key":"10.1016\/j.engappai.2026.115265_b35","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1007\/s44438-026-00023-5","article-title":"Vehicle lightweighting for carbon neutrality: decarbonization mechanisms, key processes and engineering applications","volume":"2","author":"Wang","year":"2026","journal-title":"Carbon Neutral Syst."},{"issue":"2","key":"10.1016\/j.engappai.2026.115265_b36","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1007\/s10915-022-01881-0","article-title":"Improved architectures and training algorithms for deep operator networks","volume":"92","author":"Wang","year":"2022","journal-title":"J. Sci. Comput."},{"issue":"3\u20134","key":"10.1016\/j.engappai.2026.115265_b37","doi-asserted-by":"crossref","first-page":"643","DOI":"10.1016\/S0925-2312(02)00632-X","article-title":"Determination of the spread parameter in the Gaussian kernel for classification and regression","volume":"55","author":"Wang","year":"2003","journal-title":"Neurocomputing"},{"key":"10.1016\/j.engappai.2026.115265_b38","doi-asserted-by":"crossref","DOI":"10.1080\/27525783.2026.2614885","article-title":"The digital twin-enabled deformation prediction and control methodologies for thin-walled parts in intelligent manufacturing: a review","author":"Wang","year":"2026","journal-title":"Digit. Twin"},{"issue":"3","key":"10.1016\/j.engappai.2026.115265_b39","first-page":"3862","article-title":"Transfer kernel learning for multi-source transfer gaussian process regression","volume":"45","author":"Wei","year":"2022","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"10.1016\/j.engappai.2026.115265_b40","series-title":"Scaling limits of wide neural networks with weight sharing: Gaussian process behavior, gradient independence, and neural tangent kernel derivation","author":"Yang","year":"2019"}],"container-title":["Engineering Applications of Artificial Intelligence"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0952197626015496?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0952197626015496?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,7,4]],"date-time":"2026-07-04T14:39:32Z","timestamp":1783175972000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0952197626015496"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,10]]},"references-count":40,"alternative-id":["S0952197626015496"],"URL":"https:\/\/doi.org\/10.1016\/j.engappai.2026.115265","relation":{},"ISSN":["0952-1976"],"issn-type":[{"value":"0952-1976","type":"print"}],"subject":[],"published":{"date-parts":[[2026,10]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Gaussian kernel Deep Operator Network for dynamic response prediction on variable three-dimensional geometries","name":"articletitle","label":"Article Title"},{"value":"Engineering Applications of Artificial Intelligence","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.engappai.2026.115265","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"115265"}}