{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,14]],"date-time":"2026-04-14T07:49:33Z","timestamp":1776152973799,"version":"3.50.1"},"reference-count":64,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,3,19]],"date-time":"2026-03-19T00:00:00Z","timestamp":1773878400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000835","name":"University of Bath","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100000835","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100014013","name":"UK Research and Innovation","doi-asserted-by":"publisher","award":["EP\/S031316\/1"],"award-info":[{"award-number":["EP\/S031316\/1"]}],"id":[{"id":"10.13039\/100014013","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":[[2026,6]]},"DOI":"10.1016\/j.engappai.2026.114490","type":"journal-article","created":{"date-parts":[[2026,3,21]],"date-time":"2026-03-21T04:28:22Z","timestamp":1774067302000},"page":"114490","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["Multi-Fidelity deep learning for predicting the nonlinear buckling behaviour of concrete thin-shells"],"prefix":"10.1016","volume":"174","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1894-1998","authenticated-orcid":false,"given":"Maxime","family":"Pollet","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7078-4232","authenticated-orcid":false,"given":"Paul","family":"Shepherd","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4918-7665","authenticated-orcid":false,"given":"Will","family":"Hawkins","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/j.engappai.2026.114490_b1","doi-asserted-by":"crossref","DOI":"10.1016\/j.autcon.2023.105053","article-title":"Architectural layout generation using a graph-constrained conditional generative adversarial network (GAN)","volume":"155","author":"Aalaei","year":"2023","journal-title":"Autom. Constr."},{"issue":"1","key":"10.1016\/j.engappai.2026.114490_b2","doi-asserted-by":"crossref","first-page":"198","DOI":"10.5334\/bc.59","article-title":"Embodied carbon of concrete in buildings: Part 1 - analysis of published EPD","volume":"1","author":"Anderson","year":"2020","journal-title":"Build. Cities"},{"key":"10.1016\/j.engappai.2026.114490_b3","series-title":"ANSYS Mechanical APDL Structural Analysis Guide","author":"ANSYS Inc.","year":"2012"},{"issue":"5","key":"10.1016\/j.engappai.2026.114490_b4","doi-asserted-by":"crossref","first-page":"1654","DOI":"10.3390\/s21051654","article-title":"A machine learning approach as a surrogate for a finite element analysis: Status of research and application to one dimensional systems","volume":"21","author":"Badarinath","year":"2021","journal-title":"Sens."},{"issue":"2","key":"10.1016\/j.engappai.2026.114490_b5","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1260\/0266351991494759","article-title":"A general finite element approach to the form finding of tensile structures by the updated reference strategy","volume":"14","author":"Bletzinger","year":"1999","journal-title":"Int. J. Space Struct."},{"key":"10.1016\/j.engappai.2026.114490_b6","series-title":"Shell Structures for Architecture: Form Finding and Optimization","first-page":"45","article-title":"Computational form finding and optimization","author":"Bletzinger","year":"2014"},{"key":"10.1016\/j.engappai.2026.114490_b7","series-title":"BS EN 1990:2002 +A1:2005: Eurocode - Basis of Structural Design","author":"British Standards Institution","year":"2005"},{"key":"10.1016\/j.engappai.2026.114490_b8","series-title":"BS EN 1992-1-1:2004+A1:2014, Eurocode 2: Design of Concrete Structures. General Rules and Rules for Buildings","author":"British Standards Institution","year":"2014"},{"key":"10.1016\/j.engappai.2026.114490_b9","doi-asserted-by":"crossref","first-page":"405","DOI":"10.4028\/www.scientific.net\/KEM.348-349.405","article-title":"Study of optimized steel truss design using neural network to resist lateral loads","volume":"348\u2013349","author":"Cho","year":"2007","journal-title":"Key Eng. Mater."},{"issue":"7","key":"10.1016\/j.engappai.2026.114490_b10","doi-asserted-by":"crossref","first-page":"917","DOI":"10.1016\/j.engstruct.2004.02.010","article-title":"Shear design procedure for reinforced normal and high-strength concrete beams using artificial neural networks. Part I: beams without stirrups","volume":"26","author":"Cladera","year":"2004","journal-title":"Eng. Struct."},{"key":"10.1016\/j.engappai.2026.114490_b11","doi-asserted-by":"crossref","first-page":"351","DOI":"10.3934\/acse.2023015","article-title":"Review of multi-fidelity models","volume":"1","author":"Fern\u00e1ndez-Godino","year":"2024","journal-title":"Adv. Comput. Sci. Eng."},{"key":"10.1016\/j.engappai.2026.114490_b12","doi-asserted-by":"crossref","first-page":"3567","DOI":"10.1098\/rsta.2010.0051","article-title":"Black-box calibration for complex-system simulation","volume":"368","author":"Forrester","year":"2010","journal-title":"Philos. Trans. R. Soc. A"},{"key":"10.1016\/j.engappai.2026.114490_b13","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1016\/j.advengsoft.2014.11.003","article-title":"Performance-based optimum seismic design of steel structures by a modified firefly algorithm and a new neural network","volume":"81","author":"Gholizadeh","year":"2015","journal-title":"Adv. Eng. Softw."},{"key":"10.1016\/j.engappai.2026.114490_b14","series-title":"Proceedings of the 13th International Conference on Artificial Intelligence and Statistics (AISTATS) 2010, Chia la- Guna Resort, Sardinia, Italy","article-title":"Understanding the difficulty of training deep feedforward neural networks","author":"Glorot","year":"2010"},{"key":"10.1016\/j.engappai.2026.114490_b15","series-title":"Deep Learning","author":"Goodfellow","year":"2016"},{"key":"10.1016\/j.engappai.2026.114490_b16","first-page":"2672","article-title":"Generative adversarial networks","volume":"3","author":"Goodfellow","year":"2014","journal-title":"Sci. Robot."},{"key":"10.1016\/j.engappai.2026.114490_b17","doi-asserted-by":"crossref","first-page":"3610","DOI":"10.1111\/mice.13236","article-title":"Intelligent design of shear wall layout based on diffusion models","volume":"39","author":"Gu","year":"2024","journal-title":"Comput.-Aided Civ. Infrastruct. Eng."},{"issue":"6","key":"10.1016\/j.engappai.2026.114490_b18","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1016\/S0045-7949(02)00451-0","article-title":"Neural networks applications in concrete structures","volume":"81","author":"Hadi","year":"2003","journal-title":"Comput. Struct."},{"key":"10.1016\/j.engappai.2026.114490_b19","doi-asserted-by":"crossref","first-page":"54509","DOI":"10.1109\/ACCESS.2023.3282453","article-title":"A machine learning-based surrogate finite element model for estimating dynamic response of mechanical systems","volume":"11","author":"Hashemi","year":"2023","journal-title":"IEEE Access"},{"key":"10.1016\/j.engappai.2026.114490_b20","series-title":"The Elements of Statistical Learning: Data Mining, Inference, and Prediction","author":"Hastie","year":"2017"},{"key":"10.1016\/j.engappai.2026.114490_b21","article-title":"Denoising diffusion probabilistic models","volume":"2020-December","author":"Ho","year":"2020","journal-title":"Adv. Neural Inf. Process. Syst."},{"issue":"5","key":"10.1016\/j.engappai.2026.114490_b22","doi-asserted-by":"crossref","DOI":"10.1115\/1.4049805","article-title":"StressGAN: A generative deep learning model for two-dimensional stress distribution prediction","volume":"88","author":"Jiang","year":"2021","journal-title":"J. Appl. Mech. Trans. ASME"},{"key":"10.1016\/j.engappai.2026.114490_b23","series-title":"Surrogate Model-Based Engineering Design and Optimization","author":"Jiang","year":"2020"},{"key":"10.1016\/j.engappai.2026.114490_b24","series-title":"Principal Component Analysis","author":"Jolliffe","year":"2002"},{"key":"10.1016\/j.engappai.2026.114490_b25","series-title":"Monte Carlo Methods: Second Edition","author":"Kalos","year":"2009"},{"issue":"2","key":"10.1016\/j.engappai.2026.114490_b26","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s00158-023-03734-2","article-title":"Combined shape and topology optimisation of shell structures using FE-based parameterisations","volume":"67","author":"Kamper","year":"2024","journal-title":"Struct. Multidiscip. Optim."},{"issue":"1","key":"10.1016\/j.engappai.2026.114490_b27","doi-asserted-by":"crossref","DOI":"10.1155\/2012\/712974","article-title":"Prediction of optimal design and deflection of space structures using neural networks","volume":"2012","author":"Kamyab Moghadas","year":"2012","journal-title":"Math. Probl. Eng."},{"key":"10.1016\/j.engappai.2026.114490_b28","series-title":"pyansys: Pythonic interface to MAPDL (0.60.3)","author":"Kaszynski","year":"2021"},{"issue":"17","key":"10.1016\/j.engappai.2026.114490_b29","doi-asserted-by":"crossref","first-page":"1561","DOI":"10.1016\/S0045-7949(01)00034-7","article-title":"Design of double layer grids using backpropagation neural networks","volume":"79","author":"Kaveh","year":"2001","journal-title":"Comput. Struct."},{"key":"10.1016\/j.engappai.2026.114490_b30","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1093\/biomet\/87.1.1","article-title":"Predicting the output from a complex computer code when fast approximations are available","volume":"87","author":"Kennedy","year":"2000","journal-title":"Biometrika"},{"key":"10.1016\/j.engappai.2026.114490_b31","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1561\/2200000056","article-title":"An introduction to variational autoencoders","volume":"12","author":"Kingma","year":"2019","journal-title":"Found. Trends Mach. Learn."},{"issue":"24","key":"10.1016\/j.engappai.2026.114490_b32","doi-asserted-by":"crossref","first-page":"13709","DOI":"10.1007\/s00500-022-07362-8","article-title":"Recent advances and applications of surrogate models for finite element method computations: a review","volume":"26","author":"Kudela","year":"2022","journal-title":"Soft Comput."},{"key":"10.1016\/j.engappai.2026.114490_b33","doi-asserted-by":"crossref","DOI":"10.1063\/5.0188386","article-title":"Variable-fidelity surrogate model based on transfer learning and its application in multidisciplinary design optimization of aircraft","volume":"36","author":"Leng","year":"2024","journal-title":"Phys. Fluids"},{"key":"10.1016\/j.engappai.2026.114490_b34","doi-asserted-by":"crossref","DOI":"10.1063\/5.0076538","article-title":"Multi-fidelity convolutional neural network surrogate model for aerodynamic optimization based on transfer learning","volume":"33","author":"Liao","year":"2021","journal-title":"Phys. Fluids"},{"key":"10.1016\/j.engappai.2026.114490_b35","doi-asserted-by":"crossref","DOI":"10.1016\/j.oceaneng.2021.110239","article-title":"Multi-fidelity Co-kriging surrogate model for ship hull form optimization","volume":"243","author":"Liu","year":"2022","journal-title":"Ocean Eng."},{"key":"10.1016\/j.engappai.2026.114490_b36","series-title":"Practical Finite Element Analysis for Mechanical Engineers","author":"Madier","year":"2021"},{"key":"10.1016\/j.engappai.2026.114490_b37","doi-asserted-by":"crossref","DOI":"10.1016\/j.finel.2021.103572","article-title":"A machine learning-based surrogate model for optimization of truss structures with geometrically nonlinear behavior","volume":"196","author":"Mai","year":"2021","journal-title":"Finite Elem. Anal. Des."},{"key":"10.1016\/j.engappai.2026.114490_b38","doi-asserted-by":"crossref","DOI":"10.1016\/j.jcp.2019.109020","article-title":"A composite neural network that learns from multifidelity data: Application to function approximation and inverse PDE problems","volume":"401","author":"Meng","year":"2020","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.engappai.2026.114490_b39","unstructured":"Moritomo, Y., Fujita, S., 2020. Predicting the structural behavior of geometrical nonlinearity of shell structures by machine learning. In: Proceedings of IASS Annual Symposia."},{"key":"10.1016\/j.engappai.2026.114490_b40","doi-asserted-by":"crossref","DOI":"10.1016\/j.conbuildmat.2023.130670","article-title":"Early estimation of the long-term deflection of reinforced concrete beams using surrogate models","volume":"370","author":"Nguyen","year":"2023","journal-title":"Constr. Build. Mater."},{"issue":"1","key":"10.1016\/j.engappai.2026.114490_b41","doi-asserted-by":"crossref","DOI":"10.1115\/1.4044097","article-title":"Stress field prediction in cantilevered structures using convolutional neural networks","volume":"20","author":"Nie","year":"2020","journal-title":"J. Comput. Inf. Sci. Eng."},{"key":"10.1016\/j.engappai.2026.114490_b42","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1016\/j.engappai.2018.01.006","article-title":"Generalizable surrogate model features to approximate stress in 3D trusses","volume":"71","author":"Nourbakhsh","year":"2018","journal-title":"Eng. Appl. Artif. Intell."},{"issue":"12","key":"10.1016\/j.engappai.2026.114490_b43","first-page":"943","article-title":"An introduction to convolutional neural networks","volume":"10","author":"O\u2019Shea","year":"2015","journal-title":"Int. J. Res. Appl. Sci. Eng. Technol."},{"key":"10.1016\/j.engappai.2026.114490_b44","doi-asserted-by":"crossref","first-page":"124","DOI":"10.1016\/j.istruc.2023.01.063","article-title":"A prototype low-carbon segmented concrete shell building floor system","volume":"49","author":"Oval","year":"2023","journal-title":"Structures"},{"key":"10.1016\/j.engappai.2026.114490_b45","unstructured":"Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A., 2017. Automatic differentiation in PyTorch. In: 31st Conference on Neural Information Processing Systems. NIPS 2017."},{"key":"10.1016\/j.engappai.2026.114490_b46","unstructured":"Pfaff, T., Fortunato, M., Sanchez-Gonzalez, A., Battaglia, P.W., 2021. Learning Mesh-Based Simulation With Graph Networks. Tech. Rep., URL https:\/\/sites.google.com\/view\/meshgraphnets."},{"key":"10.1016\/j.engappai.2026.114490_b47","doi-asserted-by":"crossref","DOI":"10.1016\/j.compstruc.2025.108042","article-title":"Fast structural analysis of concrete thin-shells using deep learning","volume":"320","author":"Pollet","year":"2026","journal-title":"Comput. Struct."},{"issue":"6","key":"10.1016\/j.engappai.2026.114490_b48","doi-asserted-by":"crossref","DOI":"10.2514\/2.2062","article-title":"Continuum topology optimization of buckling-sensitive structures","volume":"41","author":"Rahmatalla","year":"2003","journal-title":"AIAA J."},{"issue":"2","key":"10.1016\/j.engappai.2026.114490_b49","doi-asserted-by":"crossref","first-page":"178","DOI":"10.1016\/0141-0296(91)90050-M","article-title":"On shape finding methods and ultimate load analyses of reinforced concrete shells","volume":"13","author":"Ramm","year":"1991","journal-title":"Eng. Struct."},{"key":"10.1016\/j.engappai.2026.114490_b50","article-title":"A finite element-convolutional neural network model (FE-CNN) for stress field analysis around arbitrary inclusions","volume":"4","author":"Rezasefat","year":"2023","journal-title":"Mach. Learn.: Sci. Technol."},{"key":"10.1016\/j.engappai.2026.114490_b51","series-title":"Shell Structures for Architecture: Form Finding and Optimization","first-page":"171","article-title":"Discrete topology optimization: connectivity for gridshells","author":"Richardson","year":"2014"},{"issue":"11\u201312","key":"10.1016\/j.engappai.2026.114490_b52","doi-asserted-by":"crossref","first-page":"757","DOI":"10.1016\/j.advengsoft.2005.03.022","article-title":"Optimum design of structures by an improved genetic algorithm using neural networks","volume":"36","author":"Salajegheh","year":"2005","journal-title":"Adv. Eng. Softw."},{"key":"10.1016\/j.engappai.2026.114490_b53","series-title":"Towards Radical Regeneration: Design Modelling Symposium Berlin 2022","first-page":"108","article-title":"Augmented intelligence for architectural design with conditional autoencoders: Semiramis case study","author":"Salamanca","year":"2023"},{"key":"10.1016\/j.engappai.2026.114490_b54","series-title":"2nd International Conference on Learning Representations, ICLR 2014 - Conference Track Proceedings","article-title":"Exact solutions to the nonlinear dynamics of learning in deep linear neural networks","author":"Saxe","year":"2013"},{"key":"10.1016\/j.engappai.2026.114490_b55","series-title":"Springer Series in Geomechanics and Geoengineering","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1007\/978-3-319-00318-4_2","article-title":"Concrete and reinforced concrete behaviour","author":"Tejchman","year":"2013"},{"issue":"1","key":"10.1016\/j.engappai.2026.114490_b56","article-title":"Transfer learning based variable-fidelity surrogate model for shell buckling prediction","volume":"273","author":"Tian","year":"2021","journal-title":"Compos. Struct."},{"issue":"6","key":"10.1016\/j.engappai.2026.114490_b57","doi-asserted-by":"crossref","first-page":"1650","DOI":"10.1016\/j.engstruct.2010.02.013","article-title":"Shape and size optimisation of concrete shells","volume":"32","author":"Tom\u00e1s","year":"2010","journal-title":"Eng. Struct."},{"key":"10.1016\/j.engappai.2026.114490_b58","doi-asserted-by":"crossref","first-page":"885","DOI":"10.1080\/0305215X.2014.941290","article-title":"Improving variable-fidelity modelling by exploring global design space and radial basis function networks for aerofoil design","volume":"47","author":"Tyan","year":"2015","journal-title":"Eng. Optim."},{"key":"10.1016\/j.engappai.2026.114490_b59","unstructured":"University of Bath, Research computing group. http:\/\/dx.doi.org\/10.15125\/b6cd-s854."},{"key":"10.1016\/j.engappai.2026.114490_b60","series-title":"Enhancing Surrogate Models of Engineering Structures with Graph-Based and Physics-Informed Learning","author":"Whalen","year":"2021"},{"key":"10.1016\/j.engappai.2026.114490_b61","series-title":"Shell Structures for Architecture: Form Finding and Optimization","first-page":"239","article-title":"The multihalle and the british museum: a comparison of two gridshells","author":"Williams","year":"2014"},{"key":"10.1016\/j.engappai.2026.114490_b62","series-title":"Shell Structures for Architecture: Form Finding and Optimization","first-page":"21","article-title":"What is a shell?","author":"Williams","year":"2014"},{"key":"10.1016\/j.engappai.2026.114490_b63","series-title":"Shell Structures for Architecture: Form Finding and Optimization","first-page":"181","article-title":"Multi-criteria gridshell optimization: structural lattices on freeform surfaces","author":"Winslow","year":"2014"},{"key":"10.1016\/j.engappai.2026.114490_b64","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1016\/j.aiopen.2021.01.001","article-title":"Graph neural networks: A review of methods and applications","volume":"1","author":"Zhou","year":"2020","journal-title":"AI Open"}],"container-title":["Engineering Applications of Artificial Intelligence"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0952197626007712?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0952197626007712?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,4,14]],"date-time":"2026-04-14T06:54:54Z","timestamp":1776149694000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0952197626007712"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,6]]},"references-count":64,"alternative-id":["S0952197626007712"],"URL":"https:\/\/doi.org\/10.1016\/j.engappai.2026.114490","relation":{},"ISSN":["0952-1976"],"issn-type":[{"value":"0952-1976","type":"print"}],"subject":[],"published":{"date-parts":[[2026,6]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Multi-Fidelity deep learning for predicting the nonlinear buckling behaviour of concrete thin-shells","name":"articletitle","label":"Article Title"},{"value":"Engineering Applications of Artificial Intelligence","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.engappai.2026.114490","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 The Authors. Published by Elsevier Ltd.","name":"copyright","label":"Copyright"}],"article-number":"114490"}}