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Virtual, Digital and Hybrid Twins: A New Paradigm in Data-Based Engineering and Engineered Data

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Abstract

Engineering is evolving in the same way than society is doing. Nowadays, data is acquiring a prominence never imagined. In the past, in the domain of materials, processes and structures, testing machines allowed extract data that served in turn to calibrate state-of-the-art models. Some calibration procedures were even integrated within these testing machines. Thus, once the model had been calibrated, computer simulation takes place. However, data can offer much more than a simple state-of-the-art model calibration, and not only from its simple statistical analysis, but from the modeling and simulation viewpoints. This gives rise to the the family of so-called twins: the virtual, the digital and the hybrid twins. Moreover, as discussed in the present paper, not only data serve to enrich physically-based models. These could allow us to perform a tremendous leap forward, by replacing big-data-based habits by the incipient smart-data paradigm.

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Notes

  1. There seems to be no consensus on the definition of the concepts of virtual, digital and hybrid twins. In this paper we suggest one possible distinction, that seems feasible, attending to their respective characteristics. It is not the sole possibility, of course, nor do we pretend to create any controversy on it.

References

  1. Hey T, Tansley S, Tolle K (2009) The fourth paradigm: data-intensive scientific discovery. Microsoft Research, Redmond

    Google Scholar 

  2. Darema F (2015) DDDAS: a key driver for large-scale-big-data and large-scale-big-computing. In: Koziel S, Leifsson L, Lees M, Krzhizhanovskaya VV, Dongarra J, Sloot PMA (eds) International conference on computational science, ICCS 2015 computational science at the gates of nature, volume 51 of Procedia computer science. Elsevier, Univ Amsterdam, NTU Singapore, Univ Tennessee, 2015. 15th annual international conference on computational science (ICCS), Reykjavik Univ, Reykjavik, ICELAND, June 01–03, 2015

  3. Chinesta F, Huerta A, Rozza G, Willcox K (2017) Model reduction methods. American Cancer Society, Atlanta, pp 1–36

    Google Scholar 

  4. Chinesta F, Ladeveze P, Cueto E (2011) A short review on model order reduction based on proper generalized decomposition. Arch Comput Methods Eng 18:395–404

    Google Scholar 

  5. Chinesta F, Leygue A, Bordeu F, Aguado JV, Cueto E, Gonzalez D, Alfaro I, Ammar A, Huerta A (2013) PGD-based computational vademecum for efficient design, optimization and control. Arch Comput Methods Eng 20(1):31–59

    MathSciNet  MATH  Google Scholar 

  6. Chinesta F, Ladeveze P (eds) (2014) Separated representations and PGD-based model reduction. Springer, New York

    MATH  Google Scholar 

  7. Chinesta F, Cueto E (2014) PGD-based modeling of materials, structures and processes. Springer, Dordrecht

    Google Scholar 

  8. Cueto E, González D, Alfaro I (2016) Proper generalized decompositions: an introduction to computer implementation with matlab. SpringerBriefs in Applied Sciences and Technology. Springer, New York

    MATH  Google Scholar 

  9. Chinesta F, Keunings R, Leygue A (2014) The proper generalized decomposition for advanced numerical simulations. Springer, Dordrecht

    MATH  Google Scholar 

  10. Ghnatios C, Masson F, Huerta A, Leygue A, Cueto E, Chinesta F (2012) Proper generalized decomposition based dynamic data-driven control of thermal processes. Comput Methods Appl Mech Eng 213–216:29–41

    Google Scholar 

  11. Quaranta G, Abisset-Chavanne E, Chinesta F, Duval J-L (2018) A cyber physical system approach for composite part: From smart manufacturing to predictive maintenance. In: AIP conference proceedings, 1960(1):020025

  12. González D, Badías A, Alfaro I, Chinesta F, Cueto E (2017) Model order reduction for real-time data assimilation through extended Kalman filters. Comput Methods Appl Mech Eng 326(Supplement C):679–693

    MathSciNet  Google Scholar 

  13. Soize C, Farhat C (2016) Nonparametric probabilistic approach of model uncertainties introduced by a projection-based nonlinear reduced-order model. In: Papadrakakis M, Papadopoulos V, Stefanou G, Plevris V (eds) ECCOMAS 2016, 7th European congress on computational methods in applied sciences and engineering, Proceedings of ECCOMAS 2016, Island of Crete, Greece, June 2016, Semi-Plenary Lecture, pp 1–26

  14. Kirchdoerfer T, Ortiz M (2016) Data-driven computational mechanics. Comput Methods Appl Mech Eng 304:81–101

    MathSciNet  MATH  Google Scholar 

  15. González D, Chinesta F, Cueto E (2018) Thermodynamically consistent data-driven computational mechanics. Contin Mech Thermodyn. https://doi.org/10.1007/s00161-018-0677-z

    Article  Google Scholar 

  16. Ibañez R, Abisset-Chavanne E, Ammar A, González D, Cueto E, Huerta A, Duval JL, Chinesta F (2018) A multi-dimensional data-driven sparse identification technique: the sparse proper generalized decomposition. Complexity 2018:5608286. https://doi.org/10.1155/2018/5608286

    MATH  Google Scholar 

  17. Barrault M, Maday Y, Nguyen NC, Patera AT (2004) An ‘empirical interpolation’ method: application to efficient reduced-basis discretization of partial differential equations. Comptes Rendus Mathematique 339(9):667–672

    MathSciNet  MATH  Google Scholar 

  18. Aguado JV, Borzacchiello D, Kollepara K, Chinesta F, Huerta A (2018) Tensor representation of non-linear models using cross approximations. J Sci Comput (in press)

  19. Ladeveze P (1999) Nonlinear computational structural mechanics. Springer, New York

    MATH  Google Scholar 

  20. Bognet B, Bordeu F, Chinesta F, Leygue A, Poitou A (2012) Advanced simulation of models defined in plate geometries: 3D solutions with 2D computational complexity. Comput Methods Appl Mech Eng 201–204:1–12

    MATH  Google Scholar 

  21. Bognet B, Leygue A, Chinesta F (2014) Separated representations of 3D elastic solutions in shell geometries. Adv Model Simul Eng Sci 1(1):1–34

    MATH  Google Scholar 

  22. Bordeu F, Ghnatios C, Boulze D, Carles B, Sireude D, Leygue A, Chinesta F (2015) Parametric 3D elastic solutions of beams involved in frame structures. Adv Aircr Spacecr Sci 2(3):233–248

    Google Scholar 

  23. Chinesta F, Leygue A, Bognet B, Ghnatios C, Poulhaon F, Bordeu F, Barasinski A, Poitou A, Chatel S, Maison-Le-Poec S (2014) First steps towards an advanced simulation of composites manufacturing by automated tape placement. Int J Mater Form 7(1):81–92

    Google Scholar 

  24. González D, Alfaro I, Quesada C, Cueto E, Chinesta F (2015) Computational vademecums for the real-time simulation of haptic collision between nonlinear solids. Comput Methods Appl Mech Eng 283:210–223

    Google Scholar 

  25. Borzacchiello D, Aguado JV, Chinesta F (2017) Non-intrusive sparse subspace learning for parametrized problems. Arch Comput Methods Eng. https://doi.org/10.1007/s11831-017-9241-4

    Article  Google Scholar 

  26. Ibañez R, Abisset-Chavanne E, Chinesta F, Huerta A, Cueto E (2018) A local, multiple proper generalized decomposition based on the partition of unity. Int J Numer Methods Eng (submitted)

  27. Ghnatios C, Chinesta F, Cueto E, Leygue A, Poitou A, Breitkopf P, Villon P (2011) Methodological approach to efficient modeling and optimization of thermal processes taking place in a die: application to pultrusion. Compos Part A Appl Sci Manuf 42(9):1169–1178

    Google Scholar 

  28. Nouy A (2010) Proper generalized decompositions and separated representations for the numerical solution of high dimensional stochastic problems. Arch Comput Methods Eng 17(4):403–434

    MathSciNet  MATH  Google Scholar 

  29. Nadal E, Chinesta F, Díez P, Fuenmayor FJ, Denia FD (2015) Real time parameter identification and solution reconstruction from experimental data using the proper generalized decomposition. Comput Methods Appl Mech Eng 296:113–128

    MathSciNet  MATH  Google Scholar 

  30. Gonzalez D, Masson F, Poulhaon F, Cueto E, Chinesta F (2012) Proper generalized decomposition based dynamic data driven inverse identification. Math Comput Simul 82:1677–1695

    MathSciNet  Google Scholar 

  31. Poulhaon F, Leygue A, Rauch M, Hascoet J-Y, Chinesta F (2014) Simulation-based adaptative toolpath generation in milling processes. Int J Mach Mach Mater 15(3–4):263–284 PMID: 60552

    Google Scholar 

  32. Miller RN, Carter EF, Blue ST (1999) Data assimilation into nonlinear stochastic models. Tellus A 51(2):167–194

    Google Scholar 

  33. Chinesta F, Abisset-Chavanne E, Aguado JA, Borzacchiello D, Lopez E, Barasinski A, Gonzalez D, Cueto E, Ghnatios C, Duval JL (2018) Big-data, machine learning, data-based models and data-driven simulations, avatars and internet of things. Boarding on the 4th industrial revolution. In: Modeles: Succes et Limites. CNRS Academie des Sciences, France

  34. Badías A, Alfaro I, González D, Chinesta F, Cueto E (2018) Reduced order modeling for physically-based augmented reality. Comput Methods Appl Mech Eng 341:53–70

    MathSciNet  Google Scholar 

  35. Lake BM, Ullman TD, Tenenbaum JB, Gershman SJ (2017) Building machines that learn and think like people. Behav Brain Sci 40:e253

    Google Scholar 

  36. González D, Cueto E, Chinesta F (2015) Computational patient avatars for surgery planning. Ann Biomed Eng 44(1):35–45

    Google Scholar 

  37. González D, Aguado JV, Cueto E, Abisset-Chavanne E, Chinesta F (2016) KPCA-based parametric solutions within the PGD framework. Arch Comput Methods Eng 25(1):69–86

    MathSciNet  MATH  Google Scholar 

  38. Lee JA, Verleysen M (2007) Nonlinear dimensionality reduction. Springer, New York

    MATH  Google Scholar 

  39. Kambhatla N, Leen TK (1997) Dimension reduction by local principal component analysis. Neural Comput 9(7):1493–1516

    Google Scholar 

  40. Zhang Z, Zha H (2005) Principal manifolds and nonlinear dimensionality reduction via tangent space alignment. SIAM J Sci Comput 26(1):313–338

    MathSciNet  MATH  Google Scholar 

  41. Schölkopf B, Smola A, Müller K-R (1998) Nonlinear component analysis as a kernel eigenvalue problem. Neural Comput 10(5):1299–1319

    Google Scholar 

  42. Scholkopf B, Smola A, Muller KR (1999) Kernel principal component analysis. In: Advances in kernel methods—support vector learning. MIT Press, Cambridge, pp 327–352

  43. Roweis ST, Saul LK (2000) Nonlinear dimensionality reduction by locally linear embedding. Science 290(5500):2323–2326

    Google Scholar 

  44. Collins JP (2010) Sailing on an ocean of 0s and 1s. Science 327(5972):1455–1456

    Google Scholar 

  45. Holdren JP, Thomas K, Cyrus W, Laurie L (2014) Materials genome initiative strategic plan. Technical report, National Science and Technology Council

  46. Mellody M (2014) Big data in materials research and development: summary of a workshop. Technical report, The National Academies Press

  47. Rajan K (2005) Materials informatics. Mater Today 8(10):38–45

    Google Scholar 

  48. Brunton SL, Proctor JL, Nathan KJ (2016) Discovering governing equations from data by sparse identification of nonlinear dynamical systems. In: Proceedings of the national academy of sciences

  49. Peherstorfer B, Willcox K (2015) Dynamic data-driven reduced-order models. Comput Methods Appl Mech Eng 291:21–41

    MathSciNet  MATH  Google Scholar 

  50. Peherstorfer B, Willcox K (2016) Data-driven operator inference for nonintrusive projection-based model reduction. Comput Methods Appl Mech Eng 306:196–215

    MathSciNet  Google Scholar 

  51. Cooreman S, Lecompte D, Sol H, Vantomme J, Debruyne D (2007) Elasto-plastic material parameter identification by inverse methods: calculation of the sensitivity matrix. Int J Solids Struct 44(13):4329–4341

    MATH  Google Scholar 

  52. Shi Y, Sol H, Hua H (2006) Material parameter identification of sandwich beams by an inverse method. J Sound Vib 290(3):1234–1255

    Google Scholar 

  53. Hartmann S, Gibmeier J, Scholtes B (2006) Experiments and material parameter identification using finite elements. Uniaxial tests and validation using instrumented indentation tests. Exp Mech 46(1):5–18

    Google Scholar 

  54. Mahnken R, Stein E (1996) A unified approach for parameter identification of inelastic material models in the frame of the finite element method. Comput Methods Appl Mech Eng 136(3):225–258

    MATH  Google Scholar 

  55. Mahnken R, Stein E (1994) The identification of parameters for visco-plastic models via finite-element methods and gradient methods. Model Simul Mater Sci Eng 2(3A):597

    Google Scholar 

  56. Mahnken R, Stein E (1996) Parameter identification for viscoplastic models based on analytical derivatives of a least-squares functional and stability investigations. Int J Plast 12(4):451–479

    MATH  Google Scholar 

  57. Mahnken R, Stein E (1997) Parameter identification for finite deformation elasto-plasticity in principal directions. Comput Methods Appl Mech Eng 147(1):17–39

    MATH  Google Scholar 

  58. Yvonnet J, Gonzalez D, He Q-C (2009) Numerically explicit potentials for the homogenization of nonlinear elastic heterogeneous materials. Comput Methods Appl Mech Eng 198(33):2723–2737

    MATH  Google Scholar 

  59. Clément A, Soize C, Yvonnet J (2012) Computational nonlinear stochastic homogenization using a nonconcurrent multiscale approach for hyperelastic heterogeneous microstructures analysis. Int J Numer Methods Eng 91(8):799–824

    Google Scholar 

  60. Le BA, Yvonnet J, He QC (2015) Computational homogenization of nonlinear elastic materials using neural networks. Int J Numer Methods Eng 104(12):1061–1084

    MathSciNet  MATH  Google Scholar 

  61. Yvonnet J, Monteiro E, He Q-C (2013) Computational homogenization method and reduced database model for hyperelastic heterogeneous structures. Int J Multiscale Comput Eng 11(3):201–225

    Google Scholar 

  62. Bessa MA, Bostanabad R, Liu Z, Hu A, Apley DW, Brinson C, Chen W, Liu WK (2017) A framework for data-driven analysis of materials under uncertainty: countering the curse of dimensionality. Comput Methods Appl Mech Eng 320:633–667

    MathSciNet  Google Scholar 

  63. Liu Z, Bessa MA, Liu WK (2016) Self-consistent clustering analysis: an efficient multi-scale scheme for inelastic heterogeneous materials. Comput Methods Appl Mech Eng 306:319–341

    MathSciNet  Google Scholar 

  64. Hartigan JA, Wong MA (1979) Algorithm as 136: a k-means clustering algorithm. J R Stat Soc Ser C (Appl Stat) 28(1):100–108

    MATH  Google Scholar 

  65. Liu Z, Fleming M, Liu WK (2018) Microstructural material database for self-consistent clustering analysis of elastoplastic strain softening materials. Comput Methods Appl Mech Eng 330:547–577

    MathSciNet  Google Scholar 

  66. Kirchdoerfer T, Ortiz M (2017) Data driven computing with noisy material data sets. Comput Methods Appl Mech Eng 326:622–641

    MathSciNet  Google Scholar 

  67. Kirchdoerfer T, Ortiz M (2018) Data driven computing in dynamics. Int J Numer Methods Eng 113(11):1697–1710

    MathSciNet  Google Scholar 

  68. Ayensa-Jiménez J, Doweidar MH, Sanz-Herrera JA, Doblaré M (2018) A new reliability-based data-driven approach for noisy experimental data with physical constraints. Comput Methods Appl Mech Eng 328:752–774

    MathSciNet  Google Scholar 

  69. Ibañez R, Abisset-Chavanne E, Aguado JV, Gonzalez D, Cueto E, Chinesta F (2018) A manifold learning approach to data-driven computational elasticity and inelasticity. Arch Comput Methods Eng 25(1):47–57

    MathSciNet  MATH  Google Scholar 

  70. Ladeveze P (1985) On a family of algorithms for structural mechanics (in french). Comptes Rendus Académie des Sciences Paris 300(2):41–44

    MathSciNet  MATH  Google Scholar 

  71. Ladeveze P (1989) The large time increment method for the analyze of structures with nonlinear constitutive relation described by internal variables. Comptes Rendus Académie des Sciences Paris 309:1095–1099

    MATH  Google Scholar 

  72. Lopez E, Gonzalez D, Aguado JV, Abisset-Chavanne E, Cueto E, Binetruy C, Chinesta F (2016) A manifold learning approach for integrated computational materials engineering. Arch Comput Methods Eng 25(1):59–68

    MathSciNet  MATH  Google Scholar 

  73. Ibañez R, Borzacchiello D, Aguado JV, Abisset-Chavanne E, Cueto E, Ladeveze P, Chinesta F (2017) Data-driven non-linear elasticity: constitutive manifold construction and problem discretization. Comput Mech 60(5):813–826

    MathSciNet  MATH  Google Scholar 

  74. Sussman T, Bathe K-J (1987) A finite element formulation for nonlinear incompressible elastic and inelastic analysis. Comput Struct 26(1):357–409

    MATH  Google Scholar 

  75. Latorre M, Montáns FJ (2013) Extension of the Sussman–Bathe spline-based hyperelastic model to incompressible transversely isotropic materials. Comput Struct 122:13–26

    Google Scholar 

  76. Latorre M, Montáns FJ (2014) What-you-prescribe-is-what-you-get orthotropic hyperelasticity. Comput Mech 53(6):1279–1298

    MathSciNet  MATH  Google Scholar 

  77. Zhang M, Benítez JM, Montáns FJ (2016) Capturing yield surface evolution with a multilinear anisotropic kinematic hardening model. Int J Solids Struct 81:329–336

    Google Scholar 

  78. Crespo J, Latorre M, Montáns FJ (2017) Wypiwyg hyperelasticity for isotropic, compressible materials. Comput Mech 59(1):73–92

    MathSciNet  MATH  Google Scholar 

  79. Latorre M, Peña E, Montáns FJ (2017) Determination and finite element validation of the wypiwyg strain energy of superficial fascia from experimental data. Ann Biomed Eng 45(3):799–810

    Google Scholar 

  80. Latorre M, Montáns FJ (2017) Wypiwyg hyperelasticity without inversion formula: application to passive ventricular myocardium. Comput Struct 185:47–58

    Google Scholar 

  81. Latorre M, Montáns FJ (2018) Experimental data reduction for hyperelasticity. Comput Struct. https://doi.org/10.1016/j.compstruc.2018.02.011

    Article  Google Scholar 

  82. Grmela M, Öttinger HC (1997) Dynamics and thermodynamics of complex fluids. I. Development of a general formalism. Phys. Rev. E 56:6620–6632

    MathSciNet  Google Scholar 

  83. Oettinger HC (2005) Beyond equilibrium thermodynamics. Wiley, New York

    Google Scholar 

  84. Laso M, Öttinger HC (1993) Calculation of viscoelastic flow using molecular models: the connffessit approach. J Non-Newton Fluid Mech 47:1–20

    MATH  Google Scholar 

  85. Romero I (2009) Thermodynamically consistent time-stepping algorithms for non-linear thermomechanical systems. Int J Numer Methods Eng 79(6):706–732

    MathSciNet  MATH  Google Scholar 

  86. Romero I (2010) Algorithms for coupled problems that preserve symmetries and the laws of thermodynamics: Part I: monolithic integrators and their application to finite strain thermoelasticity. Comput Methods Appl Mech Eng 199(25–28):1841–1858

    MathSciNet  MATH  Google Scholar 

  87. Ibanez R, Abisset-Chavanne E, Gonzalez D, Duval JL, Cueto E, Chinesta F (2018) Hybrid constitutive modeling: data-driven learning of corrections to plasticity models. Int J Mater Forming (accepted for publication),

  88. Parsa B, Rajasekaran K, Meier F, Banerjee AG (2018) A hierarchical Bayesian linear regression model with local features for stochastic dynamics approximation. arXiv preprint arXiv:1807.03931

  89. Criminisi A, Shotton J, Konukoglu E (2011) Decision forests for classification, regression, density estimation, manifold learning and semi-supervised learning. Technical report, Microsoft report TR-2011-114

  90. Goodfellow I, Bengio Y, Courville A (2016) Deep learning. MIT Press, Cambridge

    MATH  Google Scholar 

  91. Raissi M, Perdikaris P, Karniadakis GE (2017) Physics informed deep learning (part I): data-driven solutions of nonlinear partial differential equations. ArXiv preprint arXiv:1711.10561

  92. Raissi M, Perdikaris P, Karniadakis GE (2017) Physics informed deep learning (part II): data-driven discovery of nonlinear partial differential equations. ArXiv preprint arXiv:1711.10566

  93. Moitra A (2018) Algorithmic aspects of machine learning. SIAM J Sci Comput 26(1):313–338

    MATH  Google Scholar 

  94. Anandkumar A, Ge R, Hsu D, Kakade SM, Telgarsky M (2014) Tensor decompositions for learning latent variable models. J Mach Learn Res 15(1):2773–2832

    MathSciNet  MATH  Google Scholar 

  95. van der Maaten L, Hinton G (2008) Visualizing data using t-SNE. J Mach Learn Res 9(Nov):2579–2605

    MATH  Google Scholar 

  96. Forgy E (1965) Cluster analysis of multivariate data: efficiency versus interpretability of classification. Biometrics 21(3):768–769

    Google Scholar 

  97. Theodoridis S, Koutroumbas K (2009) Pattern recognition. Elsevier, Amsterdam

    MATH  Google Scholar 

  98. Cristianini N, Shawe-Taylor J (2000) An introduction to support vector machines: and other kernel-based learning methods. Cambridge University Press, New York

    MATH  Google Scholar 

  99. Carlsson G (2014) Topological pattern recognition for point cloud data. Acta Numerica 23:289–368

    MathSciNet  MATH  Google Scholar 

  100. Wasserman L (2018) Topological data analysis. Ann Rev Stat Its Appl 5(1):501–532

    MathSciNet  Google Scholar 

  101. Schmid PJ (2010) Dynamic mode decomposition of numerical and experimental data. J Fluid Mech 656(August):5–28

    MathSciNet  MATH  Google Scholar 

  102. Williams MO, Kevrekidis IG, Rowley CW (2015) A data-driven approximation of the Koopman operator: extending dynamic mode decomposition. J Nonlinear Sci 25(6):1307–1346

    MathSciNet  MATH  Google Scholar 

  103. Neggers J, Allix O, Hild F, Roux S (2018) Big data in experimental mechanics and model order reduction: today’s challenges and tomorrow’s opportunities. Arch Comput Methods Eng 25(1):143–164

    MathSciNet  MATH  Google Scholar 

  104. Shaw R (1981) Strange attractors, chaotic begavior, and information flow. Zeitschrift Naturforschung Teil A 36:80–112

    MATH  Google Scholar 

  105. Guo W, Manohar K, Brunton SL, Banerjee AG (2018) Sparse-TDA: Sparse realization of topological data analysis for multi-way classification. IEEE Trans Knowl Data Eng 30(7):1403–1408

    Google Scholar 

  106. Nathan Kutz J (2013) Data-driven modeling & scientific computation: methods for complex systems & big data. Oxford University Press, Oxford

    MATH  Google Scholar 

  107. Mikolov T, Chen K, Corrado G, Dean J (2013) Efficient estimation of word representations in vector space. CoRR arXiv: abs/1301.3781

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Acknowledgements

This project has received funding from the Spanish Ministry of Economy and Competitiveness through Grants number DPI2017-85139-C2-1-R and DPI2015-72365-EXP and by the Regional Government of Aragon and the European Social Fund, research group T24 17R. Special thanks to several industrial groups and companies that contributed to the approches presented in this review article, among them, ESI, Gestamp, Volkswagen, Renault, APT, Vitirover, Airbus, Ariane, Saint Gobain, Michelin, AddUp, …

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Authors and Affiliations

  1. ENSAM ParisTech, 151 Boulevard de l’Hôpital, 75013, Paris, France

    Francisco Chinesta

  2. Aragon Institute of Engineering Research, Universidad de Zaragoza, Maria de Luna s/n, 50018, Saragossa, Spain

    Elias Cueto

  3. ESI Group Chair, Ecole Centrale de Nantes, 1 rue de la Noe, 44300, Nantes, France

    Emmanuelle Abisset-Chavanne

  4. ESI Group, 3bis rue Saarinen, 94528, Rungis Cedex, France

    Jean Louis Duval & Fouad El Khaldi

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Chinesta, F., Cueto, E., Abisset-Chavanne, E. et al. Virtual, Digital and Hybrid Twins: A New Paradigm in Data-Based Engineering and Engineered Data. Arch Computat Methods Eng 27, 105–134 (2020). https://doi.org/10.1007/s11831-018-9301-4

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