Comptes Rendus
Research article
Conciliating accuracy and efficiency to empower engineering based on performance: a short journey
Comptes Rendus. Mécanique, Online first (2023), pp. 1-13.

This paper revisits the different arts of engineering. The art of modeling for describing the behavior of complex systems from the solution of partial differential equations that are expected to govern their responses. Then, the art of simulation concerns the ability of solving these complex mathematical objects expected to describe the physical reality as accurately as possible (accuracy with respect to the exact solution of the models) and as fast as possible. Finally, the art of decision making needs to ensure accurate and fast predictions for efficient diagnosis and prognosis. For that purpose physics-informed digital twins (also known as Hybrid Twins) will be employed, allying real-time physics (where complex models are solved by using advanced model order reduction techniques) and physics-informed data-driven models for filling the gap between the reality and the physics-based model predictions. The use of physics-aware data-driven models in tandem with physics-based reduced order models allows us to predict very fast without compromising accuracy. This is compulsory for diagnosis and prognosis purposes.

Online First:
DOI: 10.5802/crmeca.188
Keywords: Physics-based modeling, Machine learning, Artificial Intelligence, Data-driven modeling, Model Order Reduction, POD, PGD, Virtual, Digital and Hybrid Twins

Francisco Chinesta 1, 2; Elias Cueto 3

1 PIMM lab, Arts et Metiers Institute of Technology, 151 Boulevard de Hôpital, 75013 Paris, France
2 CNRS@CREATE LTD, 1 Create Way, 08-01 CREATE Tower, Singapore 138602
3 Aragon Institute of Engineering Research, Universidad de Zaragoza, Maria de Luna s/n, 50018 Zaragoza, Spain
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
     author = {Francisco Chinesta and Elias Cueto},
     title = {Conciliating accuracy and efficiency to empower engineering based on performance: a short journey},
     journal = {Comptes Rendus. M\'ecanique},
     publisher = {Acad\'emie des sciences, Paris},
     year = {2023},
     doi = {10.5802/crmeca.188},
     language = {en},
     note = {Online first},
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JO  - Comptes Rendus. Mécanique
PY  - 2023
PB  - Académie des sciences, Paris
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DO  - 10.5802/crmeca.188
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%0 Journal Article
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%A Elias Cueto
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%J Comptes Rendus. Mécanique
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Francisco Chinesta; Elias Cueto. Conciliating accuracy and efficiency to empower engineering based on performance: a short journey. Comptes Rendus. Mécanique, Online first (2023), pp. 1-13. doi : 10.5802/crmeca.188.

[1] ESI Groups The History of Crash Simulation, 2019 (

[2] John A. Lee; Michel Verleysen Nonlinear dimensionality reduction, Information Science and Statistics, Springer, 2007 | DOI

[3] Sam T. Roweis; Lawrence K. Saul Nonlinear dimensionality reduction by Locally Linear Embedding, Science, Volume 290 (2000) no. 5500, pp. 2323-2326 | DOI

[4] Laurens van der Maaten; Geoffrey E. Hinton Visualizing data using t-SNE, J. Mach. Learn. Res., Volume 9 (2008), pp. 2579-2605 | Zbl

[5] Francesco Chinesta; Antonio Huerta; Gianluigi Rozza; Karen Willcox Model Order Reduction, Encyclopedia of Computational Mechanics Second Edition (Erwin Stein; Rene de Borst; Tom Hughes, eds.), John Wiley & Sons, 2017, pp. 1-36 | DOI

[6] Karen Veroy; Anthony T. Patera Certified real-time solution of the parametrized steady incompressible Navier–Stokes equations: Rigorous reduced-basis a posteriori error bounds, Int. J. Numer. Methods Fluids, Volume 47 (2005) no. 8-9, pp. 773-788 | DOI | MR | Zbl

[7] Karen Veroy; Christophe Prud’homme; Dimitrios Rovas; Anthony T. Patera A Posteriori error bounds for reduced-basis approximation of parametrized noncoercive and nonlinear elliptic partial differential equations, Proceedings of the 16th AIAA Computational Fluid Dynamics Conference, American Institute of Aeronautics and Astronautics, Inc. (2003) | DOI

[8] Yvon Maday; Anthony T. Patera; Gabriel Turinici A Priori convergence theory for reduced-basis approximations of single-parameter elliptic partial differential equations, J. Sci. Comput., Volume 17 (2002) no. 1-4, pp. 437-446 | DOI | MR | Zbl

[9] Yvon Maday; Anthony T. Patera; Gabriel Turinici Global a priori convergence theory for reduced-basis approximation of single-parameter symmetric coercive elliptic partial differential equations, C. R. Math. Acad. Sci. Paris, Volume 335 (2002) no. 3, pp. 289-294 | DOI | MR

[10] D. Ryckelynck A priori hyperreduction method: an adaptive approach, J. Comput. Phys., Volume 202 (2005) no. 1, pp. 346-366 | DOI | Zbl

[11] Todd Chapman; Philip Avery; Pat Collins; Charbel Farhat Accelerated mesh sampling for the hyper reduction of nonlinear computational models, Int. J. Num. Meth. Engrg., Volume 109 (2017) no. 12, pp. 1623-1654 | DOI | MR

[12] Maxime Barrault; Yvon Maday; Ngoc Cuong Nguyen; Anthony T. Patera An “empirical interpolation” method: Application to efficient reduced-basis discretization of partial differential equations, C. R. Math. Acad. Sci. Paris, Volume 339 (2004) no. 9, pp. 667-672 | DOI | Numdam | MR | Zbl

[13] Saifon Chaturantabut; Danny C. Sorensen Nonlinear model order reduction via discrete empirical interpolation, SIAM J. Sci. Comput., Volume 32 (2010) no. 5, pp. 2737-2764 | DOI | Zbl

[14] José V. Aguado; Domenico Borzacchiello; Kiran S. Kollepara; Francesco Chinesta; Antonio Huerta Tensor representation of on-linear models using cross approximations, J. Sci. Comput., Volume 81 (2019), pp. 22-47 | DOI | MR | Zbl

[15] Agathe Reille; Nicolas Hascoet; Chady Ghnatios; Amine Ammar; Elías Cueto; Jean-Louis Duval; Francisco Chinesta; Roland Keunings Incremental dynamic mode decomposition: A reduced-model learner operating at the low-data limit, C. R. Méc. Acad. Sci. Paris, Volume 347 (2019) no. 11, pp. 780-792 | DOI

[16] P. J. Schmid Dynamic mode decomposition of numerical and experimental data, J. Fluid Mech., Volume 656 (2010), pp. 5-28 | DOI | MR | Zbl

[17] Matthew O. Williams; Ioannis G. Kevrekidis; Clarence W. Rowley A data-driven approximation of the Koopman operator: extending dynamic mode decomposition, J. Nonlinear Sci., Volume 25 (2015) no. 6, pp. 1307-1346 | DOI | MR | Zbl

[18] Agathe Reille; Victor Champaney; Fatima Daim; Yves Tourbier; Nicolas Hascoet; David González; Elías Cueto; Jean-Louis Duval; Francisco Chinesta Learning data-driven reduced elastic and inelastic models of spot-welded patches, Mechanics & Industry,, Volume 22 (2021), 32, 17 pages | DOI

[19] Abel Sancarlos; Morgan Cameron; Jean-Marc Le Peuvedic; Juliette Groulier; Jean-Louis Duval; Elias Cueton; Francisco Chinesta Learning stable reduced-order models for hybrid twins. Data Centric Engineering, Data-Centric Engineering, Volume 2 (2021), E10 | DOI

[20] Hung V. Ly; Hien T. Tran Modeling and control of physical processes using Proper Orthogonal Decomposition, Mathematical and Computer Modelling, Volume 33 (2001) no. 1-3, pp. 223-236 | DOI | Zbl

[21] D. Amsallem; C. Farhat Interpolation method for adapting reduced-order models and application to aeroelasticity, AIAA J., Volume 46 (2008) no. 7, pp. 1803-1813 | DOI

[22] Pierre Ladevèze Nonlinear Computational Structural Mechanics. New Approaches and Non-Incremental Methods of Calculation, Mechanical Engineering Series, Springer, 1999 | DOI

[23] Francesco Chinesta; Adrien Leygue; F. Bordeu; F. Bordeu; José V. Aguado; Elías Cueto; David González; Icíar Alfaro; Amine Ammar; Antonio Huerta PGD-Based Computational Vademecum for Efficient Design, Optimization and Control, Arch. Comput. Methods Eng., Volume 20 (2013) no. 1, pp. 31-59 | DOI | MR | Zbl

[24] Francesco Chinesta; Roland Keunings; Adrien Leygue The Proper Generalized Decomposition for Advanced Numerical Simulations. A primer, SpringerBriefs in Applied Sciences and Technology, Springer, 2014 | DOI

[25] Steven L. Brunton; Joshua L. Proctor; Nathan Kutz Discovering governing equations from data by sparse identification of nonlinear dynamical systems, Proc. Natl. Acad. Sci. USA, Volume 113 (2016) no. 15, pp. 3932-3937 | DOI | MR | Zbl

[26] Robert Tibshirani Regression shrinkage and selection via the lasso, J. R. Stat. Soc., Ser. B, Stat. Methodol., Volume 58 (1996) no. 1, pp. 267-288 | DOI | MR | Zbl

[27] Domenico Borzacchiello; José V. Aguado; Francesco Chinesta Non-intrusive Sparse Subspace Learning for parametrized problems, Arch. Comput. Methods Eng., Volume 26 (2019) no. 2, pp. 303-326 | DOI | MR

[28] Rubén Ibáñez; Emmanuelle Abisset-Chavanne; Amine Ammar; David González; Elías Cueto; Antonio Huerta; Jean-Louis Duval; Francisco Chinesta A multi-dimensional data-driven sparse identification technique: the sparse Proper Generalized Decomposition, Complexity, Volume 2018 (2018), 5608286 | DOI | Zbl

[29] Abel Sancarlos; Victor Champaney; Jean-Louis Duval; Elías Cueto; Francisco Chinesta PGD-based advanced nonlinear multiparametric regressions for constructing metamodels at the scarce-data limit, Adv. Model. and Simul. in Eng. Sci., Volume 10 (2023) no. 4 | DOI

[30] Mariette Awad; Rahul Khanna Support Vector Regression, Efficient Learning Machines: Theories, Concepts, and Applications for Engineers and System Designers, Apress, 2015, pp. 67-80 | DOI

[31] Craig W. Kirkwood Decision Tree primer, 2002 (

[32] Leo Breiman Random Forests, Mach. Learn., Volume 45 (2001), pp. 5-32 | DOI | Zbl

[33] Jürgen Schmidhuber Deep learning in neural networks: An overview, Neural Netw., Volume 61 (2015), pp. 85-117 | DOI

[34] Ian Goodfellow; Yoshua Bengio; Aaron Courville Deep learning, Adaptive Computation and Machine Learning, MIT Press, 2016

[35] Maziar Raissi; Paris Perdikaris; George Em. Karniadakis Physics informed deep learning (part I): data-driven solutions of nonlinear partial differential equations (2017) (

[36] Maziar Raissi; Paris Perdikaris; George Em. Karniadakis Physics informed deep learning (part II): data-driven discovery of nonlinear partial differential equations (2017) (

[37] David González; Francesco Chinesta; Elías Cueto Thermodynamically consistent data-driven computational mechanics, Comput. Mech., Volume 31 (2019), pp. 239-253 | DOI | MR

[38] David González; Francesco Chinesta; Elías Cueto Learning corrections for hyper-elastic models from data, Front. Mater., Volume 6 (2019) | DOI

[39] Quercus Hernandez; Alberto Badias; David González; Francesco Chinesta; Elías Cueto Deep learning of thermodynamics-aware reduced-order models from data, Comput. Methods Appl. Mech. Eng., Volume 379 (2021), 113763 | DOI | MR | Zbl

[40] Quercus Hernandez; David González; Francesco Chinesta; Elías Cueto Learning non-Markovian physics from data, Journal of Computational Physics, Volume 428 (2021), 109982 | DOI | MR

[41] Beatriz Moya; David González; Icíar Alfaro; Francisco Chinesta; Elías Cueto Learning slosh dynamics by means of data, Comput. Mech., Volume 64 (2019), pp. 511-523 | DOI | MR | Zbl

[42] Beatriz Moya; Alberto Badías; Icíar Alfaro; Francisco Chinesta; Elías Cueto Digital twins that learn and correct themselves, Int. J. Numer. Methods Eng., Volume 123 (2020) no. 13, pp. 3034-3044 | DOI

[43] Miroslav Grmela; Hans Christian Öttinger Dynamics and thermodynamics of complex fluids. I. Development of a general formalism, Phys. Rev. E, Volume 56 (1997) no. 6, pp. 6620-6632 | DOI | MR

[44] Ruben Ibanez; Pierre Gilormini; Elías Cueto; Francisco Chinesta Numerical experiments on unsupervised manifold learning applied to mechanical modeling of materials and structures, Comptes Rendus. Mécanique, Volume 348 (2020) no. 10-11, pp. 937-958 | DOI

[45] Geoffrey E. Hinton; Richard Zemel Autoencoders, minimum description length and Helmholtz free energy, Advances in Neural Information Processing Systems, Volume 6, Morgan-Kaufmann, 1993, pp. 3-10

[46] Francesco Chinesta; Elías Cueto; Emmanuelle Abisset-Chavanne; Jean-Louis Duval; Fouad El Khaldi Virtual, Digital and Hybrid Twins: A New Paradigm in Data-Based Engineering and Engineered Data, Arch. Comput. Methods Eng., Volume 27 (2020), pp. 105-134 | DOI | MR

[47] Alberto Badias; S. Curtit; David González; Icíar Alfaro; Francesco Chinesta; Elías Cueto An Augmented Reality platform for interactive aerodynamic design and analysis, Int. J. Numer. Methods Eng., Volume 138 (2019), pp. 125-138 | DOI | MR

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