{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,13]],"date-time":"2026-08-13T17:30:53Z","timestamp":1786642253468,"version":"build-2736575974"},"reference-count":44,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Expert Systems with Applications"],"published-print":{"date-parts":[[2027,1]]},"DOI":"10.1016\/j.eswa.2026.133907","type":"journal-article","created":{"date-parts":[[2026,8,4]],"date-time":"2026-08-04T15:14:43Z","timestamp":1785856483000},"page":"133907","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"PC","title":["Semi-parametric Bayesian physics-informed neural network-based digital twin for dynamical systems"],"prefix":"10.1016","volume":"333","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-2141-9261","authenticated-orcid":false,"given":"Aneela","family":"Shaheen","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Babar","family":"Zaman","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shahab","family":"Nadir","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Faraz","family":"Mukhtiar","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Naveed","family":"Razzaq Butt","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"key":"10.1016\/j.eswa.2026.133907_bib0001","doi-asserted-by":"crossref","DOI":"10.1016\/j.eswa.2025.128358","article-title":"Digital twins for smart asset management in the energy industry: State-of-the-art","volume":"289","author":"Amin","year":"2025","journal-title":"Expert Systems with Applications"},{"issue":"7","key":"10.1016\/j.eswa.2026.133907_bib0002","doi-asserted-by":"crossref","first-page":"2115","DOI":"10.3390\/s24072115","article-title":"Integration of railway bridge structural health monitoring into the internet of things with a digital twin: A case study","volume":"24","author":"Armijo","year":"2024","journal-title":"Sensors"},{"key":"10.1016\/j.eswa.2026.133907_bib0003","unstructured":"Arup (2019). Digital twin: Towards a meaningful framework. Technical Report, Arup, London, England."},{"key":"10.1016\/j.eswa.2026.133907_bib0004","article-title":"Application of digital twin in structural health monitoring of civil structures: A systematic literature review based on PRISMA","author":"Azanaw","year":"2025","journal-title":"SSRN Electronic Journal"},{"key":"10.1016\/j.eswa.2026.133907_bib0005","doi-asserted-by":"crossref","DOI":"10.1016\/j.compstruc.2020.106410","article-title":"Machine learning based digital twin for dynamical systems with multiple time-scales","volume":"243","author":"Chakraborty","year":"2021","journal-title":"Computers & Structures"},{"key":"10.1016\/j.eswa.2026.133907_bib0006","doi-asserted-by":"crossref","DOI":"10.1016\/j.neucom.2023.126327","article-title":"Deep neural networks in the cloud: Review, applications, challenges and research directions","volume":"545","author":"Chan","year":"2023","journal-title":"Neurocomputing"},{"key":"10.1016\/j.eswa.2026.133907_bib0007","doi-asserted-by":"crossref","DOI":"10.1016\/j.eswa.2023.122422","article-title":"An optimisation-based digital twin for automated operation of rail level crossings","volume":"239","author":"Djordjevi\u0107","year":"2024","journal-title":"Expert Systems with Applications"},{"issue":"3","key":"10.1016\/j.eswa.2026.133907_bib0008","doi-asserted-by":"crossref","DOI":"10.12688\/digitaltwin.17599.3","article-title":"The development of a digital twin concept system","volume":"2","author":"Duan","year":"2025","journal-title":"Digital Twin"},{"issue":"3","key":"10.1016\/j.eswa.2026.133907_bib0009","doi-asserted-by":"crossref","first-page":"1534","DOI":"10.3390\/ai5030074","article-title":"Understanding physics-informed neural networks: Techniques, applications, trends, and challenges","volume":"5","author":"Farea","year":"2024","journal-title":"AI"},{"key":"10.1016\/j.eswa.2026.133907_bib0010","doi-asserted-by":"crossref","first-page":"108952","DOI":"10.1109\/ACCESS.2020.2998358","article-title":"Digital twin: Enabling technologies, challenges and open research","volume":"8","author":"Fuller","year":"2020","journal-title":"IEEE Access"},{"key":"10.1016\/j.eswa.2026.133907_bib0011","series-title":"Digital twin: A dynamic system and computing perspective","author":"Ganguli","year":"2023"},{"key":"10.1016\/j.eswa.2026.133907_bib0012","unstructured":"Ganguly, A., & Earp, S. W. F. (2021). An introduction to variational inference. arXiv preprint arXiv: 2108.13083."},{"key":"10.1016\/j.eswa.2026.133907_bib0013","doi-asserted-by":"crossref","unstructured":"Gij\u00f3n, A., Manjavacas, A., Bottaccioli, L., Lanzini, A., Molina-Solana, M., & G\u00f3mez-Romero, J. (2024). Explainable hybrid semi-parametric model for prediction of power generated by wind turbines. 14836, 264\u2013277. 10.1007\/978-3-031-63775-9_21.","DOI":"10.1007\/978-3-031-63775-9_21"},{"issue":"358","key":"10.1016\/j.eswa.2026.133907_bib0014","first-page":"1","article-title":"Optimal parameter-transfer learning by semiparametric model averaging","volume":"24","author":"Hu","year":"2023","journal-title":"Journal of Machine Learning Research"},{"key":"10.1016\/j.eswa.2026.133907_bib0015","doi-asserted-by":"crossref","DOI":"10.1016\/j.iswa.2025.200516","article-title":"Digital twins: Recent advances and future directions in engineering fields","volume":"26","author":"Iranshahi","year":"2025","journal-title":"Intelligent Systems with Applications"},{"issue":"2","key":"10.1016\/j.eswa.2026.133907_bib0016","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1109\/MCI.2022.3155327","article-title":"Hands-on Bayesian neural networks-a tutorial for deep learning users","volume":"17","author":"Jospin","year":"2022","journal-title":"IEEE Computational Intelligence Magazine"},{"key":"10.1016\/j.eswa.2026.133907_bib0017","doi-asserted-by":"crossref","DOI":"10.1016\/j.compchemeng.2025.109119","article-title":"Incorporating first-principles information into hybrid modeling structures: Comparing hybrid semi-parametric models with physics-informed recurrent neural networks","volume":"199","author":"Jul-Rasmussen","year":"2025","journal-title":"Computers & Chemical Engineering"},{"issue":"1","key":"10.1016\/j.eswa.2026.133907_bib0018","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1609\/aaai.v37i1.25074","article-title":"A semi-parametric model for decision making in high-dimensional sensory discrimination tasks","volume":"37","author":"Keeley","year":"2023","journal-title":"Proceedings of the AAAI Conference on Artificial Intelligence"},{"key":"10.1016\/j.eswa.2026.133907_bib0019","unstructured":"Kennedy, E. H. (2017). Semiparametric theory. arXiv preprint arXiv: 1709.06418."},{"key":"10.1016\/j.eswa.2026.133907_bib0020","doi-asserted-by":"crossref","first-page":"1781","DOI":"10.69997\/sct.101576","article-title":"Physics-informed graph neural networks for modeling spatially distributed dynamically operated processes","volume":"4","author":"Khalid","year":"2025","journal-title":"Systems and Control Transactions"},{"issue":"9","key":"10.1016\/j.eswa.2026.133907_bib0021","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1007\/s00158-022-03348-0","article-title":"Data-driven prognostics with low-fidelity physical information for digital twin: Physics-informed neural network","volume":"65","author":"Kim","year":"2022","journal-title":"Structural and Multidisciplinary Optimization"},{"key":"10.1016\/j.eswa.2026.133907_bib0022","doi-asserted-by":"crossref","DOI":"10.1016\/j.cosrev.2020.100341","article-title":"Machine learning and deep learning in smart manufacturing: The smart grid paradigm","volume":"40","author":"Kotsiopoulos","year":"2021","journal-title":"Computer Science Review"},{"key":"10.1016\/j.eswa.2026.133907_bib0023","article-title":"A Physics-Informed Neural Network (PINN) framework for generic bioreactor modelling","volume":"203","author":"Kumar Thirugnanasambandam","year":"2025","journal-title":"Computers & Chemical Engineering"},{"key":"10.1016\/j.eswa.2026.133907_bib0024","doi-asserted-by":"crossref","DOI":"10.1016\/j.cma.2022.115346","article-title":"Bayesian physics informed neural networks for real-world nonlinear dynamical systems","volume":"402","author":"Linka","year":"2022","journal-title":"Computer Methods in Applied Mechanics and Engineering"},{"key":"10.1016\/j.eswa.2026.133907_bib0025","doi-asserted-by":"crossref","DOI":"10.1016\/j.eswa.2026.131140","article-title":"Digital twin-driven dynamic prediction of operation status and process optimization for flexible production line","volume":"308","author":"Meng","year":"2026","journal-title":"Expert Systems with Applications"},{"issue":"2","key":"10.1016\/j.eswa.2026.133907_bib0026","doi-asserted-by":"crossref","first-page":"665","DOI":"10.5267\/j.msl.2011.11.001","article-title":"A semi parametric approach to dual modeling","volume":"2","author":"Navaee","year":"2002","journal-title":"Management Science Letters"},{"key":"10.1016\/j.eswa.2026.133907_bib0027","doi-asserted-by":"crossref","first-page":"764","DOI":"10.30574\/wjarr.2025.25.1.3821","article-title":"Digital twin applications for predicting and controlling vibrations in manufacturing systems","volume":"25","author":"Okpala","year":"2025","journal-title":"World Journal of Advanced Research and Reviews"},{"key":"10.1016\/j.eswa.2026.133907_bib0028","doi-asserted-by":"crossref","DOI":"10.1016\/j.jcp.2023.112342","article-title":"Adaptive weighting of Bayesian physics informed neural networks for multitask and multiscale forward and inverse problems","volume":"491","author":"Perez","year":"2023","journal-title":"Journal of Computational Physics"},{"issue":"7","key":"10.1016\/j.eswa.2026.133907_bib0029","first-page":"579","article-title":"Multilayer perceptron and neural networks","volume":"8","author":"Popescu","year":"2009","journal-title":"WSEAS Transactions on Circuits and Systems"},{"key":"10.1016\/j.eswa.2026.133907_bib0030","unstructured":"Raissi, M., Perdikaris, P., & Karniadakis, G. E. (2017). Physics informed deep learning (Part I): Data-driven solutions of nonlinear partial differential equations. arXiv preprint arXiv: 1711.10561."},{"key":"10.1016\/j.eswa.2026.133907_bib0031","doi-asserted-by":"crossref","first-page":"686","DOI":"10.1016\/j.jcp.2018.10.045","article-title":"Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations","volume":"378","author":"Raissi","year":"2019","journal-title":"Journal of Computational Physics"},{"key":"10.1016\/j.eswa.2026.133907_bib0032","unstructured":"Rasheed, A., San, O., & Kvamsdal, T. (2019). Digital twin: Values, challenges and enablers. arXiv preprint arXiv: 1910.01719."},{"key":"10.1016\/j.eswa.2026.133907_bib0033","unstructured":"Riedel, S., & Stulp, F. (2019). Comparing semi-parametric model learning algorithms for dynamic model estimation in robotics. arXiv preprint arXiv: 1906.11909."},{"key":"10.1016\/j.eswa.2026.133907_bib0034","doi-asserted-by":"crossref","DOI":"10.1016\/j.ymssp.2021.107614","article-title":"Digital twin, physics-based model, and machine learning applied to damage detection in structures","volume":"155","author":"Ritto","year":"2021","journal-title":"Mechanical Systems and Signal Processing"},{"issue":"2","key":"10.1016\/j.eswa.2026.133907_bib0035","doi-asserted-by":"crossref","first-page":"9195","DOI":"10.1016\/j.ifacol.2020.12.2182","article-title":"Modeling system dynamics with physics-informed neural networks based on lagrangian mechanics","volume":"53","author":"Roehrl","year":"2020","journal-title":"IFAC-PapersOnLine"},{"key":"10.1016\/j.eswa.2026.133907_bib0036","unstructured":"Sani, N., Lee, J., Nabi, R., & Shpitser, I. (2020). A semiparametric approach to interpretable machine learning. arXiv preprint arXiv: 2006.04732."},{"key":"10.1016\/j.eswa.2026.133907_bib0037","doi-asserted-by":"crossref","DOI":"10.1016\/j.eswa.2024.125207","article-title":"Physics-informed neural network classification framework for reliability analysis","volume":"258","author":"Shi","year":"2024","journal-title":"Expert Systems with Applications"},{"key":"10.1016\/j.eswa.2026.133907_bib0038","doi-asserted-by":"crossref","DOI":"10.1016\/j.eswa.2025.126390","article-title":"A fast, information-interactive, and reservoir computing-based digital twin for high-rise building operation","volume":"269","author":"Tan","year":"2025","journal-title":"Expert Systems with Applications"},{"key":"10.1016\/j.eswa.2026.133907_bib0039","doi-asserted-by":"crossref","first-page":"20418","DOI":"10.1109\/ACCESS.2017.2756069","article-title":"Digital twin shop-floor: A new shop-floor paradigm towards smart manufacturing","volume":"5","author":"Tao","year":"2017","journal-title":"IEEE Access"},{"issue":"2","key":"10.1016\/j.eswa.2026.133907_bib0040","doi-asserted-by":"crossref","first-page":"29","DOI":"10.3390\/designs8020029","article-title":"Aircraft structural design and life-cycle assessment through digital twins","volume":"8","author":"Tavares","year":"2024","journal-title":"Designs"},{"key":"10.1016\/j.eswa.2026.133907_bib0041","doi-asserted-by":"crossref","DOI":"10.1016\/j.eswa.2024.124678","article-title":"Physics-informed machine learning: A comprehensive review on applications in anomaly detection and condition monitoring","volume":"255","author":"Wu","year":"2024","journal-title":"Expert Systems with Applications"},{"key":"10.1016\/j.eswa.2026.133907_bib0042","doi-asserted-by":"crossref","DOI":"10.1016\/j.jcp.2020.109913","article-title":"B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data","volume":"425","author":"Yang","year":"2021","journal-title":"Journal of Computational Physics"},{"key":"10.1016\/j.eswa.2026.133907_bib0043","doi-asserted-by":"crossref","DOI":"10.1016\/j.cma.2024.117075","article-title":"Data-driven physics-informed neural networks: A digital twin perspective","volume":"428","author":"Yang","year":"2024","journal-title":"Computer Methods in Applied Mechanics and Engineering"},{"issue":"1","key":"10.1016\/j.eswa.2026.133907_bib0044","doi-asserted-by":"crossref","first-page":"1149","DOI":"10.1007\/s00170-018-1617-6","article-title":"Digital twin-based smart production management and control framework for the complex product assembly shop-floor","volume":"96","author":"Zhuang","year":"2018","journal-title":"The International Journal of Advanced Manufacturing Technology"}],"container-title":["Expert Systems with Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0957417426028150?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0957417426028150?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,8,13]],"date-time":"2026-08-13T16:43:26Z","timestamp":1786639406000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0957417426028150"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2027,1]]},"references-count":44,"alternative-id":["S0957417426028150"],"URL":"https:\/\/doi.org\/10.1016\/j.eswa.2026.133907","relation":{},"ISSN":["0957-4174"],"issn-type":[{"value":"0957-4174","type":"print"}],"subject":[],"published":{"date-parts":[[2027,1]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Semi-parametric Bayesian physics-informed neural network-based digital twin for dynamical systems","name":"articletitle","label":"Article Title"},{"value":"Expert Systems with Applications","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.eswa.2026.133907","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":"133907"}}