Review Article Open Access

Model Updating and Data Assimilation in Engineering Digital Twins: A Cross-Domain Critical Review of Methods, Evidence, and Validation

International Journal of Digital Technology Driven Engineering Vol. 1 No. 1 (2026): Inaugural Issue Published 2026-08-06 DOI pending
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Abstract

Engineering Digital Twins rely on the continuous alignment of virtual models with evolving physical systems, yet the computational mechanisms that enable this alignment are often described inconsistently and assessed with uneven standards of evidence. This review critically examines model updating and data assimilation as the principal physical-to-virtual synchronization mechanisms of engineering Digital Twins across structural, manufacturing, aerospace, thermal, energy, robotic, and built-environment applications. Particular attention is given to the quantities being updated, including dynamic states, physical parameters, unknown inputs, boundary conditions, model structure, and model-form discrepancy, as well as to the temporal regime in which updating is performed. The synthesis shows that no inference method is universally preferable. Deterministic and finite-element updating provide transparent solutions for interpretable batch calibration; Bayesian approaches support uncertainty-aware parameter and discrepancy estimation; Kalman and particle-filter methods enable sequential state and parameter assimilation; and reduced-order, surrogate, and hybrid models address the computational demands of operational deployment. Method suitability depends on identifiability, model fidelity, nonlinearity, observation cadence, computational cost, uncertainty structure, interpretability requirements, and the consequence of prediction error. Across application domains, the most credible studies combine a complete physical-observation loop with independent or changed-condition validation, explicit uncertainty treatment, defensible latency assessment, and clearly defined applicability limits. Recurring weaknesses include conflation of calibration with validation, unsupported real-time claims, incomplete treatment of model-form error, and limited reproducibility. The review develops a unified taxonomy, an evidence-based method-selection framework, a validation-maturity hierarchy, and reporting guidance for the development of credible, continuously evaluated, and decision-relevant engineering Digital Twins.

Declarations

Author contributions
S.K.G.: Conceptualization, Methodology, Investigation, Data curation, Formal analysis, Visualization, Writing—original draft, and Writing—review and editing. N.D.L.: Methodology, Validation, Supervision, and Writing—review and editing.
Data availability
Data are available from the corresponding author upon reasonable request.
Declaration of generative AI assistance
Generative AI tools were used to support language editing, document structuring, visual preparation, and bibliographic workflow management. The authors remain responsible for source verification, scientific interpretation, corpus decisions, appraisal scores, and the final manuscript.
Ethics approval and consent
Not applicable. This review synthesized published literature and did not involve human participants, animals, clinical interventions, or identifiable personal data.
Funding
This research received no external funding.
Competing interests
S.K.G. and N.D.L. are editors of IJDTDE.

References

Rasheed A, San O, Kvamsdal T. Digital Twin: Values, Challenges and Enablers From a Modeling Perspective. IEEE Access. 2020. https://doi.org/10.1109/ACCESS.2020.2970143.

Wagg DJ, Worden K, Barthorpe RJ, Gardner P. Digital Twins: State-of-the-Art and Future Directions for Modeling and Simulation in Engineering Dynamics Applications. ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B. 2020. https://doi.org/10.1115/1.4046739.

Thelen A, et al. A Comprehensive Review of Digital Twin-Part 1: Modeling and Twinning Enabling Technologies. Structural and Multidisciplinary Optimization. 2022. https://doi.org/10.1007/s00158-022-03425-4.

Thelen A, et al. A Comprehensive Review of Digital Twin-Part 2: Roles of Uncertainty Quantification and Optimization, a Battery Digital Twin, and Perspectives. Structural and Multidisciplinary Optimization. 2023. https://doi.org/10.1007/s00158-022-03410-x.

Jones D, Snider C, Nassehi A, Yon J, Hicks B. Characterising the Digital Twin: A Systematic Literature Review. CIRP Journal of Manufacturing Science and Technology. 2020;29:36–52. https://doi.org/10.1016/j.cirpj.2020.02.002.

Semeraro C, Lezoche M, Panetto H, Dassisti M. Digital Twin Paradigm: A Systematic Literature Review. Computers in Industry. 2021;130:103469. https://doi.org/10.1016/j.compind.2021.103469.

Kritzinger W, Karner M, Traar G, Henjes J, Sihn W. Digital Twin in Manufacturing: A Categorical Literature Review and Classification. IFAC-PapersOnLine. 2018;51(11):1016–1022. https://doi.org/10.1016/j.ifacol.2018.08.474.

Negri E, Fumagalli L, Macchi M. A Review of the Roles of Digital Twin in CPS-Based Production Systems. Procedia Manufacturing. 2017;11:939–948. https://doi.org/10.1016/j.promfg.2017.07.198.

Tao F, Zhang H, Liu A, Nee AYC. Digital Twin in Industry: State-of-the-Art. IEEE Transactions on Industrial Informatics. 2019;15(4):2405–2415. https://doi.org/10.1109/TII.2018.2873186.

Fuller A, Fan Z, Day C, Barlow C. Digital Twin: Enabling Technologies, Challenges and Open Research. IEEE Access. 2020;8:108952–108971. https://doi.org/10.1109/ACCESS.2020.2998358.

Cimino C, Negri E, Fumagalli L. Review of Digital Twin Applications in Manufacturing. Computers in Industry. 2019;113:103130. https://doi.org/10.1016/j.compind.2019.103130.

Madni AM, Madni CC, Lucero SD. Leveraging Digital Twin Technology in Model-Based Systems Engineering. Systems. 2019;7(1):7. https://doi.org/10.3390/systems7010007.

Tao F, Qi Q, Wang L, Nee AYC. Digital Twins and Cyber–Physical Systems toward Smart Manufacturing and Industry 4.0: Correlation and Comparison. Engineering. 2019;5(4):653–661. https://doi.org/10.1016/j.eng.2019.01.014.

Glaessgen EH, Stargel DS. The Digital Twin Paradigm for Future NASA and U.S. Air Force Vehicles. In: 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference. Honolulu, HI; 2012. https://doi.org/10.2514/6.2012-1818.

Tuegel EJ, Ingraffea AR, Eason TG, Spottswood SM. Reengineering Aircraft Structural Life Prediction Using a Digital Twin. International Journal of Aerospace Engineering. 2011;2011:154798. https://doi.org/10.1155/2011/154798.

Wright L, Davidson S. How to Tell the Difference Between a Model and a Digital Twin. Advanced Modeling and Simulation in Engineering Sciences. 2020;7:13. https://doi.org/10.1186/s40323-020-00147-4.

Schleich B, Anwer N, Mathieu L, Wartzack S. Shaping the Digital Twin for Design and Production Engineering. CIRP Annals. 2017;66(1):141–144. https://doi.org/10.1016/j.cirp.2017.04.040.

National Academies of Sciences, Engineering, and Medicine. Foundational Research Gaps and Future Directions for Digital Twins. Washington, DC: The National Academies Press; 2024. https://doi.org/10.17226/26894.

Ljung L. Perspectives on System Identification. Annual Reviews in Control. 2010;34(1):1–12. https://doi.org/10.1016/j.arcontrol.2009.12.001.

Farrar CR, Worden K. An Introduction to Structural Health Monitoring. Philosophical Transactions of the Royal Society A. 2007;365(1851):303–315. https://doi.org/10.1098/rsta.2006.1928.

Worden K, Manson G. The Application of Machine Learning to Structural Health Monitoring. Philosophical Transactions of the Royal Society A. 2007;365(1851):515–537. https://doi.org/10.1098/rsta.2006.1938.

Mottershead JE, Friswell MI. Model Updating in Structural Dynamics: A Survey. Journal of Sound and Vibration. 1993;167(2):347–375. https://doi.org/10.1006/jsvi.1993.1340.

Beck JL, Katafygiotis LS. Updating Models and Their Uncertainties. I: Bayesian Statistical Framework. Journal of Engineering Mechanics. 1998;124(4):455–461. https://doi.org/10.1061/(ASCE)0733-9399(1998)124:4(455).

Katafygiotis LS, Beck JL. Updating Models and Their Uncertainties. II: Model Identifiability. Journal of Engineering Mechanics. 1998;124(4):463–467. https://doi.org/10.1061/(ASCE)0733-9399(1998)124:4(463).

Vanik MW, Beck JL, Au SK. Bayesian Probabilistic Approach to Structural Health Monitoring. Journal of Engineering Mechanics. 2000;126(7):738–745. https://doi.org/10.1061/(ASCE)0733-9399(2000)126:7(738).

Kerschen G, Worden K, Vakakis AF, Golinval JC. Past, Present and Future of Nonlinear System Identification in Structural Dynamics. Mechanical Systems and Signal Processing. 2006;20(3):505–592. https://doi.org/10.1016/j.ymssp.2005.04.008.

Kennedy MC, O'Hagan A. Bayesian Calibration of Computer Models. Journal of the Royal Statistical Society: Series B. 2001;63(3):425–464. https://doi.org/10.1111/1467-9868.00294.

Bayarri MJ, Paulo R, Berger JO, Sacks J, Cafeo JA, Cavendish J, Lin CH, Tu J. A Framework for Validation of Computer Models. Technometrics. 2007;49(2):138–154. https://doi.org/10.1198/004017007000000092.

Higdon D, Gattiker J, Williams B, Rightley M. Computer Model Calibration Using High-Dimensional Output. Journal of the American Statistical Association. 2008;103(482):570–583. https://doi.org/10.1198/016214507000000888.

Brynjarsdóttir J, O'Hagan A. Learning about Physical Parameters: The Importance of Model Discrepancy. Inverse Problems. 2014;30(11):114007. https://doi.org/10.1088/0266-5611/30/11/114007.

Plumlee M. Bayesian Calibration of Inexact Computer Models. Journal of the American Statistical Association. 2017;112(519):1274–1285. https://doi.org/10.1080/01621459.2016.1211016.

Arendt PD, Apley DW, Chen W, Lamb D, Gorsich D. Improving Identifiability in Model Calibration Using Multiple Responses. Journal of Mechanical Design. 2012;134(10):100909. https://doi.org/10.1115/1.4007573.

Gu M, Wang L. Scaled Gaussian Stochastic Process for Computer Model Calibration and Prediction. SIAM/ASA Journal on Uncertainty Quantification. 2018;6(4):1555–1583. https://doi.org/10.1137/17M1159890.

Morrison RE, Oliver TA, Moser RD. Representing Model Inadequacy: A Stochastic Operator Approach. SIAM/ASA Journal on Uncertainty Quantification. 2018;6(2):457–496. https://doi.org/10.1137/16M1106419.

Kalman RE. A New Approach to Linear Filtering and Prediction Problems. Journal of Basic Engineering. 1960;82(1):35–45. https://doi.org/10.1115/1.3662552.

Julier SJ, Uhlmann JK. Unscented Filtering and Nonlinear Estimation. Proceedings of the IEEE. 2004;92(3):401–422. https://doi.org/10.1109/JPROC.2003.823141.

Evensen G. Sequential Data Assimilation with a Nonlinear Quasi-Geostrophic Model Using Monte Carlo Methods to Forecast Error Statistics. Journal of Geophysical Research: Oceans. 1994;99(C5):10143–10162. https://doi.org/10.1029/94JC00572.

Evensen G. The Ensemble Kalman Filter: Theoretical Formulation and Practical Implementation. Ocean Dynamics. 2003;53:343–367. https://doi.org/10.1007/s10236-003-0036-9.

Arulampalam MS, Maskell S, Gordon N, Clapp T. A Tutorial on Particle Filters for Online Nonlinear/Non-Gaussian Bayesian Tracking. IEEE Transactions on Signal Processing. 2002;50(2):174–188. https://doi.org/10.1109/78.978374.

Doucet A, Godsill S, Andrieu C. On Sequential Monte Carlo Sampling Methods for Bayesian Filtering. Statistics and Computing. 2000;10(3):197–208. https://doi.org/10.1023/A:1008935410038.

Rao CV, Rawlings JB, Mayne DQ. Constrained State Estimation for Nonlinear Discrete-Time Systems: Stability and Moving Horizon Approximations. IEEE Transactions on Automatic Control. 2003;48(2):246–258. https://doi.org/10.1109/TAC.2002.808470.

Carrassi A, Bocquet M, Bertino L, Evensen G. Data Assimilation in the Geosciences: An Overview of Methods, Issues, and Perspectives. WIREs Climate Change. 2018;9(5):e535. https://doi.org/10.1002/wcc.535.

Bannister RN. A Review of Operational Methods of Variational and Ensemble-Variational Data Assimilation. Quarterly Journal of the Royal Meteorological Society. 2017;143:607–633. https://doi.org/10.1002/qj.2982.

Benner P, Gugercin S, Willcox K. A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems. SIAM Review. 2015;57(4):483–531. https://doi.org/10.1137/130932715.

Peherstorfer B, Willcox K, Gunzburger M. Survey of Multifidelity Methods in Uncertainty Propagation, Inference, and Optimization. SIAM Review. 2018;60(3):550–591. https://doi.org/10.1137/16M1082469.

Rowley CW. Model Reduction for Fluids, Using Balanced Proper Orthogonal Decomposition. International Journal of Bifurcation and Chaos. 2005;15(3):997–1013. https://doi.org/10.1142/S0218127405012429.

Oberkampf WL, Trucano TG. Verification and Validation in Computational Fluid Dynamics. Progress in Aerospace Sciences. 2002;38(3):209–272. https://doi.org/10.1016/S0376-0421(02)00005-2.

Roy CJ, Oberkampf WL. A Comprehensive Framework for Verification, Validation, and Uncertainty Quantification in Scientific Computing. Computer Methods in Applied Mechanics and Engineering. 2011;200(25–28):2131–2144. https://doi.org/10.1016/j.cma.2011.03.016.

Stuart AM. Inverse Problems: A Bayesian Perspective. Acta Numerica. 2010;19:451–559. https://doi.org/10.1017/S0962492910000061.

Kaipio J, Somersalo E. Statistical and Computational Inverse Problems. New York: Springer; 2005. https://doi.org/10.1007/b138659.

Marzouk YM, Najm HN, Rahn LA. Stochastic Spectral Methods for Efficient Bayesian Solution of Inverse Problems. Journal of Computational Physics. 2007;224(2):560–586. https://doi.org/10.1016/j.jcp.2006.10.010.

Smith RC. Uncertainty Quantification: Theory, Implementation, and Applications. Philadelphia: SIAM; 2014. https://doi.org/10.1137/1.9781611973228.

Oliver TA, Terejanu G, Simmons CS, Moser RD. Validating Predictions of Unobserved Quantities. Computer Methods in Applied Mechanics and Engineering. 2015;283:1310–1335. https://doi.org/10.1016/j.cma.2014.08.023.

Trucano TG, Swiler LP, Igusa T, Oberkampf WL, Pilch M. Calibration, Validation, and Sensitivity Analysis: What's What. Reliability Engineering & System Safety. 2006;91(10–11):1331–1357. https://doi.org/10.1016/j.ress.2005.11.031.

Es-haghi MS, Anitescu C, Rabczuk T. Methods for Enabling Real-Time Analysis in Digital Twins: A Literature Review. Computers & Structures. 2024;297:107342. https://doi.org/10.1016/j.compstruc.2024.107342.

Zech P, Barat S, Nast B, Oakes B, Michael J, Zschaler S, Barn B, Breu R. Model-Based Digital Twin Engineering: Insights, Challenges, and Future Directions. Software and Systems Modeling. 2026. https://doi.org/10.1007/s10270-026-01368-8.

Kopp L, Harfmann P, Mangaluru Ramananda A, Kley M. Digital Twins in Engineering: A Literature Review and Expert Survey for Potential Analysis. Engineering Research. 2026;90:8. https://doi.org/10.1007/s10010-026-00940-4.

Adimass SA, Żak A. Review of Digital Twin in Structural Dynamics to Improve Condition Monitoring. Structural Control and Health Monitoring. 2026;2026:2777297. https://doi.org/10.1155/stc/2777297.

Ereiz S, Duvnjak I, Jimenez-Alonso JF. Review of Finite Element Model Updating Methods for Structural Applications. Structures. 2022. https://doi.org/10.1016/j.istruc.2022.05.041.

Chen Y, et al. Finite Element Model Updating for Material Model Calibration: A Review and Guide to Practice. Archives of Computational Methods in Engineering. 2025. https://doi.org/10.1007/s11831-024-10200-9.

Page MJ, McKenzie JE, Bossuyt PM, Boutron I, Hoffmann TC, Mulrow CD, et al. The PRISMA 2020 Statement: An Updated Guideline for Reporting Systematic Reviews. BMJ. 2021;372:n71. https://doi.org/10.1136/bmj.n71.

Li Y, et al. Statistical Parameterized Physics-Based Machine Learning Digital Shadow Models for Laser Powder Bed Fusion Process. Additive Manufacturing. 2024. https://doi.org/10.1016/j.addma.2024.104214.

Liu J, et al. Deep Neural Operator Enabled Digital Twin Modeling for Additive Manufacturing. Advances in Computational Science and Engineering. 2024. https://doi.org/10.3934/acse.2024010.

Eneyew DD, Capretz MAM, Bitsuamlak GT. Continuous Model Calibration Framework for Smart-Building Digital Twin: A Generative Model-Based Approach. Applied Energy. 2024. https://doi.org/10.1016/j.apenergy.2024.124080.

Karkadakattil A. A Physics-Stabilized Self-Updating Digital Twin Framework Using Physics-Informed Neural Networks for Thermal Field Prediction. Applied Computer Systems. 2026. https://doi.org/10.2478/acss-2026-0003.

Jiang Z, Karlsson M, Agrell E, Hager C. PIDT: Physics-Informed Digital Twin for Optical Fiber Parameter Estimation. Optical Fiber Communication Conference. 2026. https://doi.org/10.1364/OFC.2026.M4K.3.

Ward R, Choudhary R, Gregory A, Jans-Singh M, Girolami M. Continuous Calibration of a Digital Twin: Comparison of Particle Filter and Bayesian Calibration Approaches. Data-Centric Engineering. 2021;2:e15. https://doi.org/10.1017/dce.2021.12.

de Angelis M, et al. Robust Online Updating of a Digital Twin with Imprecise Probability. Mechanical Systems and Signal Processing. 2023;185:109877. https://doi.org/10.1016/j.ymssp.2022.109877.

Edington T, et al. A Time-Evolving Digital Twin Tool for Engineering Dynamics Applications. Mechanical Systems and Signal Processing. 2023;185:109971. https://doi.org/10.1016/j.ymssp.2022.109971.

Kessels BM, Fey RHB, van de Wouw N. Real-Time Parameter Updating for Nonlinear Digital Twins Using Inverse Mapping Models and Transient-Based Features. Nonlinear Dynamics. 2023. https://doi.org/10.1007/s11071-023-08354-5.

Kessels BM, et al. Uncertainty Quantification in Real-Time Parameter Updating for Digital Twins Using Bayesian Inverse Mapping Models. Nonlinear Dynamics. 2025. https://doi.org/10.1007/s11071-024-10608-9.

Mucke NT, Bohte SM, Oosterlee CW. The Deep Latent Space Particle Filter for Real-Time Data Assimilation with Uncertainty Quantification. Scientific Reports. 2024. https://doi.org/10.1038/s41598-024-69901-7.

Titscher T, van Dijk T, Kadoke D, Robens-Radermacher A, Herrmann R, Unger JF. Bayesian Model Calibration and Damage Detection for a Digital Twin of a Bridge Demonstrator. Engineering Reports. 2023;5:e12669. https://doi.org/10.1002/eng2.12669.

Arcones A, et al. Model Bias Identification for Bayesian Calibration of Stochastic Digital Twins of Bridges. Applied Stochastic Models in Business and Industry. 2024. https://doi.org/10.1002/asmb.2897.

Donato L, Galletti C, Parente A. Self-Updating Digital Twin of a Hydrogen-Powered Furnace Using Data Assimilation. Applied Thermal Engineering. 2024;236:121431. https://doi.org/10.1016/j.applthermaleng.2023.121431.

Shi G, et al. Digital Twin-Based Model Updating Method for Mechanical Behaviors Analysis of Cable Truss Structure. Journal of Constructional Steel Research. 2024;220:108917. https://doi.org/10.1016/j.jcsr.2024.108917.

Tang A, Shi X, Qin G, Shi H, Mei X. A Digital Twin-Based System for Timely Simulation of Bridge Structural Performance with Finite Element Model Updating. Structure and Infrastructure Engineering. 2025. https://doi.org/10.1080/15732479.2025.2587043.

Ali H, Bocchino G, Bono F, Perotti F, Martinelli L. Finite Element Model Updating for Digital Twin Development Using Operational Modal Analysis: The JRC Atmospheric Observatory Tower Case Study. Lecture Notes in Civil Engineering. 2025. https://doi.org/10.1007/978-3-031-96110-6_32.

Xia J, et al. Digital Twin-Assisted Gearbox Dynamic Model Updating Toward Fault Diagnosis. Frontiers of Mechanical Engineering. 2023. https://doi.org/10.1007/s11465-023-0748-0.

Lang S, et al. Overcoming Uncertainty With an Ensemble of Physical Models and Real-Time Measurements: Thermal Error Compensation Using Kalman Filters in a Digital Twin. In: ICTIMT 2025 Proceedings. 2026. https://doi.org/10.1007/978-3-032-01194-7_25.

Zhuo Y, Yan B. A Key Component in Digital Twin of Aircraft Structures: Multi-Dimensional Flight-Parameter Measurements. Chinese Journal of Aeronautics. 2025. https://doi.org/10.7527/S1000-6893.2025.32375.

Kosmaga SR, et al. Digital Twin-Enabled Real-Time Parameter Estimation of a Wheeled Mobile Robot. Systems Science & Control Engineering. 2026. https://doi.org/10.1080/21642583.2026.2634459.

Zhao K, et al. Digital Twin-Supported Battery State Estimation Based on TCN-LSTM Neural Networks and Transfer Learning. CSEE Journal of Power and Energy Systems. 2025. https://doi.org/10.17775/CSEEJPES.2024.00900.

Wu T, et al. An Online Learning Method for Constructing a Self-Update Digital Twin Model for Transformer Temperature Prediction. Applied Thermal Engineering. 2024. https://doi.org/10.1016/j.applthermaleng.2023.121728.

Wang R, Zhou X, Dong L, Wen Y, Tan R, Chen L, Wang G, Zeng F. Kalibre: Knowledge-Based Neural Surrogate Model Calibration for Data Center Digital Twins. Proceedings of ACM BuildSys. 2020. https://doi.org/10.1145/3408308.3427982.

Wang J, et al. Adaptive Digital Twin Modeling with Control: Integration of Extended Kalman Filter-Based Recursive Sparse Nonlinear Identification with Model Predictive Control. Sensors. 2026;26:1734. https://doi.org/10.3390/s26051734.

Park J, Li C, Byon E, Bailey W, Hussain Q, Lonari Y. Hierarchical Parameter Calibration of Digital Twins at Ford Motor Company. INFORMS Journal on Applied Analytics. 2026. https://doi.org/10.1287/inte.2025.0259.

Li X, Ye L, Bian X. Sequential Data Assimilation for Digital Twin Modeling of Shield Tunnel Structure-Soil Interaction Systems. Tunnelling and Underground Space Technology. 2026;168(2):107168. https://doi.org/10.1016/j.tust.2025.107168.

Nóvoa A, Noiray N, Dawson JR, Magri L. A Real-Time Digital Twin of Azimuthal Thermoacoustic Instabilities. Journal of Fluid Mechanics. 2024;1001:A49. https://doi.org/10.1017/jfm.2024.1052.

Georgantzinos SK, Antoniou PA, Spitas C. A Multi-Scale Computational Framework for the Hygro-Thermo-Mechanical Analysis of Laminated Composite Structures with Carbon Nanotube Inclusions. Results in Engineering. 2023;17:100904. https://doi.org/10.1016/j.rineng.2023.100904.

Georgantzinos SK, Giannopoulos GI, Markolefas SI. Vibration Analysis of Carbon Fiber-Graphene-Reinforced Hybrid Polymer Composites Using Finite Element Techniques. Materials. 2020;13(19):4225. https://doi.org/10.3390/ma13194225.

Antoniou PA, Stamoulis KP, Georgantzinos SK. Progressive Damage and Failure Analysis of CNT-Reinforced Laminated Nanocomposite Structures: A Multiscale Modeling Framework. Engineering Failure Analysis. 2025;173:109452. https://doi.org/10.1016/j.engfailanal.2025.109452.

Brunton SL, Proctor JL, Kutz JN. Discovering Governing Equations from Data by Sparse Identification of Nonlinear Dynamical Systems. Proceedings of the National Academy of Sciences. 2016;113(15):3932–3937. https://doi.org/10.1073/pnas.1517384113.

Raissi M, Perdikaris P, Karniadakis GE. Physics-Informed Neural Networks: A Deep Learning Framework for Solving Forward and Inverse Problems Involving Nonlinear Partial Differential Equations. Journal of Computational Physics. 2019;378:686–707. https://doi.org/10.1016/j.jcp.2018.10.045.

Lu L, Jin P, Pang G, Zhang Z, Karniadakis GE. Learning Nonlinear Operators via DeepONet Based on the Universal Approximation Theorem of Operators. Nature Machine Intelligence. 2021;3:218–229. https://doi.org/10.1038/s42256-021-00302-5.

Kovachki N, Li Z, Liu B, Azizzadenesheli K, Bhattacharya K, Stuart AM, Anandkumar A. Neural Operator: Learning Maps Between Function Spaces with Applications to PDEs. Journal of Machine Learning Research. 2023;24(89):1–97.

Karniadakis GE, Kevrekidis IG, Lu L, Perdikaris P, Wang S, Yang L. Physics-Informed Machine Learning. Nature Reviews Physics. 2021;3:422–440. https://doi.org/10.1038/s42254-021-00314-5.

Voulgaris S, Chandrinos S, Chamatidis I, Kazakis G, Tsakalis P, Mitropoulou CC, Georgantzinos SK, Istrati D, Lagaros ND. Machine Learning and Data-Driven Methods for Steel Constitutive Modeling: A State-of-the-Art Review and Validation. Discover Civil Engineering. 2025;2:228. https://doi.org/10.1007/s44290-025-00389-4.

Shao G, Hightower J, Schindel W. Credibility Consideration for Digital Twins in Manufacturing. Manufacturing Letters. 2023;35:24–28. https://doi.org/10.1016/j.mfglet.2022.11.009.

Lang S, Zorzini M, Scholze S, Mayr J, Bambach M. Sensor Placement Utilizing a Digital Twin for Thermal Error Compensation of Machine Tools. Journal of Manufacturing Systems. 2025. https://doi.org/10.1016/j.jmsy.2025.03.003.

Kammer DC. Sensor Placement for On-Orbit Modal Identification and Correlation of Large Space Structures. Journal of Guidance, Control, and Dynamics. 1991;14(2):251–259. https://doi.org/10.2514/3.20635.

Papadimitriou C. Optimal Sensor Placement Methodology for Parametric Identification of Structural Systems. Journal of Sound and Vibration. 2004;278(4–5):923–947. https://doi.org/10.1016/j.jsv.2003.10.063.

Manohar K, Brunton BW, Kutz JN, Brunton SL. Data-Driven Sparse Sensor Placement for Reconstruction: Demonstrating the Benefits of Exploiting Known Patterns. IEEE Control Systems Magazine. 2018;38(3):63–86. https://doi.org/10.1109/MCS.2018.2810460.

Chaloner K, Verdinelli I. Bayesian Experimental Design: A Review. Statistical Science. 1995;10(3):273–304. https://doi.org/10.1214/ss/1177009939.

Huan X, Marzouk YM. Simulation-Based Optimal Bayesian Experimental Design for Nonlinear Systems. Journal of Computational Physics. 2013;232(1):288–317. https://doi.org/10.1016/j.jcp.2012.08.013.

Evensen G, Vossepoel FC, van Leeuwen PJ. Data Assimilation Fundamentals: A Unified Formulation of the State and Parameter Estimation Problem. Cham: Springer; 2022. https://doi.org/10.1007/978-3-030-96709-3.

Reich S, Cotter C. Probabilistic Forecasting and Bayesian Data Assimilation. Cambridge: Cambridge University Press; 2015. https://doi.org/10.1017/CBO9781107706804.

Iglesias MA, Law KJH, Stuart AM. Ensemble Kalman Methods for Inverse Problems. Inverse Problems. 2013;29(4):045001. https://doi.org/10.1088/0266-5611/29/4/045001.

Emerick AA, Reynolds AC. Ensemble Smoother with Multiple Data Assimilation. Computers & Geosciences. 2013;55:3–15. https://doi.org/10.1016/j.cageo.2012.03.011.

Houtekamer PL, Zhang F. Review of the Ensemble Kalman Filter for Atmospheric Data Assimilation. Monthly Weather Review. 2016;144(12):4489–4532. https://doi.org/10.1175/MWR-D-15-0440.1.

Lang S, Talleri S, Mayr J, Wegener K, Bambach M. Kalman Filter-Driven State Observer for Thermal Error Compensation in Machine Tool Digital Twins. Manufacturing Letters. 2024. https://doi.org/10.1016/j.mfglet.2024.09.025.

van Leeuwen PJ, Künsch HR, Nerger L, Potthast R, Reich S. Particle Filters for High-Dimensional Geoscience Applications: A Review. Quarterly Journal of the Royal Meteorological Society. 2019;145(723):2335–2365. https://doi.org/10.1002/qj.3551.

Branlard E, et al. Augmented Kalman Filter with a Reduced Mechanical Model to Estimate Tower Loads on a Land-Based Wind Turbine: A Step Towards Digital-Twin Simulations. Wind Energy Science. 2020;5:1155-1167. https://doi.org/10.5194/wes-5-1155-2020.

Haseltine EL, Rawlings JB. Critical Evaluation of Extended Kalman Filtering and Moving-Horizon Estimation. Industrial & Engineering Chemistry Research. 2005;44(8):2451–2460. https://doi.org/10.1021/ie034308l.

Rawlings JB, Bakshi BR. Particle Filtering and Moving Horizon Estimation. Computers & Chemical Engineering. 2006;30(10–12):1529–1541. https://doi.org/10.1016/j.compchemeng.2006.05.031.

Alvarez-Cuesta M, et al. Which Data Assimilation Method to Use and When. Environmental Research Letters. 2024. https://doi.org/10.1088/1748-9326/ad3143.

Willard J, Jia X, Xu S, Steinbach M, Kumar V. Integrating Scientific Knowledge with Machine Learning for Engineering and Environmental Systems. ACM Computing Surveys. 2023;55(4):66. https://doi.org/10.1145/3514228.

Duraisamy K, Iaccarino G, Xiao H. Turbulence Modeling in the Age of Data. Annual Review of Fluid Mechanics. 2019;51:357–377. https://doi.org/10.1146/annurev-fluid-010518-040547.

Quarteroni A, Manzoni A, Negri F. Reduced Basis Methods for Partial Differential Equations: An Introduction. Cham: Springer; 2016. https://doi.org/10.1007/978-3-319-15431-2.

Lee K, Carlberg KT. Model Reduction of Dynamical Systems on Nonlinear Manifolds Using Deep Convolutional Autoencoders. Journal of Computational Physics. 2020;404:108973. https://doi.org/10.1016/j.jcp.2019.108973.

Chandrinos S, Voulgaris S, Mitropoulou CC, Gkara M, Georgantzinos SK, Lagaros ND. Statistically Grounded Selection and Validation of Surrogate Models for Civil-Engineering Decision Support: ANN, Kriging and SVM Across Three Case Studies. Machine Learning for Computational Science and Engineering. 2026;2:35. https://doi.org/10.1007/s44379-026-00075-x.

Gawlikowski J, Tassi CRN, Ali M, Lee J, Humt M, Feng J, et al. A Survey of Uncertainty in Deep Neural Networks. Artificial Intelligence Review. 2023;56(Suppl 1):1513–1589. https://doi.org/10.1007/s10462-023-10562-9.

Zimmermann N, Breu T, Mayr J, Wegener K. Autonomously Triggered Model Updates for Self-Learning Thermal Error Compensation. CIRP Annals. 2021. https://doi.org/10.1016/j.cirp.2021.04.029.

Lu J, Liu A, Dong F, Gu F, Gama J, Zhang G. Learning under Concept Drift: A Review. IEEE Transactions on Knowledge and Data Engineering. 2019;31(12):2346–2363. https://doi.org/10.1109/TKDE.2018.2876857.

ASME. ASME V&V 40-2018: Assessing Credibility of Computational Modeling through Verification and Validation: Application to Medical Devices. New York: American Society of Mechanical Engineers; 2018.

Georgantzinos SK, Kastanos G, Tseni AD, Kostopoulos V. Efficient Optimization of the Multi-Response Problem in the Taguchi Method through Advanced Data Envelopment Analysis Formulations Integration. Computers & Industrial Engineering. 2024;197:110618. https://doi.org/10.1016/j.cie.2024.110618.

Georgantzinos SK, Kostopoulos G, Papadopoulou E, Voulgaris S, Tseni A, Bakalis P, Gkara MN, Mitropoulou CC, Kazakis G, Munteanu A, Gancet J, Lagaros ND. Design and Prototyping of Topology-Optimized, Additively Manufactured Lightweight Components for Space Robotic Systems: A Case Study. Advanced Engineering Materials. 2026;28(4):e202502311. https://doi.org/10.1002/adem.202502311.

Georgantzinos SK, Papadopoulou E, Bakalis P. Prediction of Anisotropic Mechanical Behavior in Fused Deposition Modeling-Printed Polylactic Acid Structures with Straight-Line Microstructure Using Taguchi Design. Journal of Materials Engineering and Performance. 2025;34(10):10218-10234. https://doi.org/10.1007/s11665-025-12381-1.

Georgantzinos SK, Papadopoulou E. Digital Twin for Fused Filament Fabrication (FFF). Zenodo; 2026. https://doi.org/10.5281/zenodo.18270596.

Georgantzinos SK, Papadopoulou E, Kostopoulos G, Voulgaris S, Tseni A, Bakalis P, Gkara M, Mitropoulou CC, Lagaros ND. A Comprehensive Review of Additive Manufacturing for Space Applications: Materials, Advances, Challenges, and Future Directions. Advanced Engineering Materials. 2025;27(22):e202501082. https://doi.org/10.1002/adem.202501082.

Torzoni M, et al. A Digital Twin Framework for Civil Engineering Structures. Computer Methods in Applied Mechanics and Engineering. 2024;418:116584. https://doi.org/10.1016/j.cma.2023.116584.

Chen H, Li W, Bao J, Shen Y. Multi-Scale Error-Triggered Latent Assimilation for Reduced-Order Digital Twins of Gas-Solid Flow Reactors. Chemical Engineering Journal. 2026. https://doi.org/10.1016/j.cej.2026.179496.

Mucke NT, Pandey P, Jain S, Bohte SM, Oosterlee CW. A Probabilistic Digital Twin for Leak Localization in Water Distribution Networks Using Generative Deep Learning. Sensors. 2023;23:6179. https://doi.org/10.3390/s23136179.

Irino N, Kobayashi A, Shinba Y, Kawai K, Spescha D, Wegener K. Digital Twin Based Accuracy Compensation. CIRP Annals. 2023. https://doi.org/10.1016/j.cirp.2023.04.088.

Rozsas A, Slobbe A, Martini G, Jansen R. Structural and Load Parameter Estimation of a Real-World Reinforced Concrete Slab Bridge Using Measurements and Bayesian Statistics. Structural Concrete. 2022. https://doi.org/10.1002/suco.202100913.

Koune I, Rozsas A, Slobbe A, Cicirello A. Bayesian System Identification for Structures Considering Spatial and Temporal Correlation. Data-Centric Engineering. 2023. https://doi.org/10.1017/dce.2023.18.

ISO. ISO 23247-1:2021, Automation Systems and Integration—Digital Twin Framework for Manufacturing—Part 1: Overview and General Principles. Geneva: International Organization for Standardization; 2021.

Mertens J, Denil J. Reusing Model Validation Methods for the Continuous Validation of Digital Twins of Cyber-Physical Systems. Software and Systems Modeling. 2025;24:1427–1449. https://doi.org/10.1007/s10270-024-01225-6.

Gama J, Žliobaitė I, Bifet A, Pechenizkiy M, Bouchachia A. A Survey on Concept Drift Adaptation. ACM Computing Surveys. 2014;46(4):44. https://doi.org/10.1145/2523813.

Xu Y, Park C. Online Bayesian Calibration under Gradual and Abrupt System Changes. arXiv preprint. 2026. https://doi.org/10.48550/arXiv.2605.06612.

Torzoni M, Maisto D, Manzoni A, Donnarumma F, Pezzulo G, Corigliano A. Active Digital Twins via Active Inference. Engineering Applications of Artificial Intelligence. 2026;174:114519. https://doi.org/10.1016/j.engappai.2026.114519.

Alexanderian A. Optimal Experimental Design for Infinite-Dimensional Bayesian Inverse Problems Governed by PDEs: A Review. Inverse Problems. 2021;37(4):043001. https://doi.org/10.1088/1361-6420/abe10c.

Shao G. Manufacturing Digital Twin Standards. In: Proceedings of the ACM/IEEE 27th International Conference on Model Driven Engineering Languages and Systems Companion. 2024:370–377. https://doi.org/10.1145/3652620.3688250.

Kibira D, Shao G. Data Requirements for a Digital Twin of a CNC Machine Tool. In: Proceedings of the 2025 Winter Simulation Conference; 7–10 December 2025; Seattle, WA, USA. Published 2026.