G. Berkooz, P. Holmes, and J. L. Lumley, The Proper Orthogonal Decomposition in the Analysis of Turbulent Flows, Annual Review of Fluid Mechanics, vol.25, issue.1, 1993.
DOI : 10.1146/annurev.fl.25.010193.002543

I. T. Jolliffe, Principal Component Analysis, Second Edition, Encycl. Stat. Behav. Sci, vol.30, issue.487, pp.10-2307, 2002.

S. Chaturantabut and D. C. Sorensen, Nonlinear Model Reduction via Discrete Empirical Interpolation, SIAM Journal on Scientific Computing, vol.32, issue.5, pp.2737-2764, 2010.
DOI : 10.1137/090766498
URL : https://scholarship.rice.edu/bitstream/1911/70218/1/ChaturantabutS.pdf

M. Barrault, Y. Maday, N. C. Nguyen, and A. T. Patera, An ???empirical interpolation??? method: application to efficient reduced-basis discretization of partial differential equations, Comptes Rendus Mathematique, vol.339, issue.9, 2004.
DOI : 10.1016/j.crma.2004.08.006
URL : https://hal.archives-ouvertes.fr/hal-00021702

D. Ryckelynck, F. Chinesta, E. Cueto, and A. Ammar, On thea priori model reduction: Overview and recent developments, Archives of Computational Methods in Engineering, vol.43, issue.5, pp.91-128, 2006.
DOI : 10.1007/3-540-27099-X_1

R. Everson and L. Sirovich, Karhunen???Lo??ve procedure for gappy data, Journal of the Optical Society of America A, vol.12, issue.8, 1995.
DOI : 10.1364/JOSAA.12.001657
URL : http://camelot.mssm.edu/publications/larry/Karhunen-Loeve.pdf

J. Fehr and D. Grunert, Model reduction and clustering techniques for crash simulations, PAMM, vol.15, issue.1, pp.125-126, 2015.
DOI : 10.1007/s11222-007-9033-z

B. Bohn, J. Garcke, R. Iza-teran, A. Paprotny, B. Peherstorfer et al., Analysis of Car Crash Simulation Data with Nonlinear Machine Learning Methods, Procedia Computer Science, vol.18, pp.621-630, 2013.
DOI : 10.1016/j.procs.2013.05.226

Y. Saad, Krylov subspace methods for solving large unsymmetric linear systems, Mathematics of Computation, vol.37, issue.155, pp.105-126, 1981.
DOI : 10.1090/S0025-5718-1981-0616364-6
URL : http://www.ams.org/mcom/1981-37-155/S0025-5718-1981-0616364-6/S0025-5718-1981-0616364-6.pdf

F. Z. Daim, D. Ryckelynck, and A. Kamoulakos, Hyper reduction for crash simulation, in: World Congr, Comput. Mech

K. Willcox, Unsteady flow sensing and estimation via the gappy proper orthogonal decomposition, Computers & Fluids, vol.35, issue.2, pp.208-226, 2006.
DOI : 10.1016/j.compfluid.2004.11.006
URL : http://dspace.mit.edu/bitstream/1721.1/3897/2/HPCES020.pdf

D. Ryckelynck, Hyper-reduction of mechanical models involving internal variables, International Journal for Numerical Methods in Engineering, vol.1, issue.3, pp.75-89, 2009.
DOI : 10.1002/nme.2406
URL : https://hal.archives-ouvertes.fr/hal-00359157

K. Carlberg, C. Bou-mosleh, and C. Farhat, Efficient non-linear model reduction via a least-squares Petrov-Galerkin projection and compressive tensor approximations, International Journal for Numerical Methods in Engineering, vol.35, issue.2
DOI : 10.1016/j.compfluid.2004.11.006

N. Verdon, C. Allery, C. Béghein, A. Hamdouni, and D. Ryckelynck, Reduced-order modelling for solving linear and non-linear equations, International Journal for Numerical Methods in Biomedical Engineering, vol.2, issue.1, pp.43-58, 2011.
DOI : 10.1007/BF02905932
URL : https://hal.archives-ouvertes.fr/hal-00541925

F. Chinesta, A. Ammar, and E. Cueto, Proper generalized decomposition of multiscale models, International Journal for Numerical Methods in Engineering, vol.197, issue.5, pp.1114-1132, 2010.
DOI : 10.1007/978-1-4612-1432-8
URL : https://hal.archives-ouvertes.fr/hal-01007222

M. Vitse, D. Néron, and P. A. Boucard, Virtual charts of solutions for parametrized nonlinear equations, Computational Mechanics, vol.13, issue.1, pp.1529-1539, 2014.
DOI : 10.1007/BF02905932
URL : https://hal.archives-ouvertes.fr/hal-01657143

L. Boucinha, A. Ammar, A. Gravouil, and A. Nouy, Ideal minimal residual-based proper generalized decomposition for non-symmetric multi-field models ??? Application to transient elastodynamics in space-time domain, Computer Methods in Applied Mechanics and Engineering, vol.273, pp.56-76, 2014.
DOI : 10.1016/j.cma.2014.01.019
URL : https://hal.archives-ouvertes.fr/hal-00952496

R. H. Myers, D. C. Montgomery, and C. M. Anderson-cook, Response surface methodology: process and product optimization using designed experiments, 2016.

N. Wiener, The Homogeneous Chaos, American Journal of Mathematics, vol.60, issue.4, pp.897-936, 1938.
DOI : 10.2307/2371268

N. Dyn, D. Levin, and S. Rippa, Numerical Procedures for Surface Fitting of Scattered Data by Radial Functions, SIAM Journal on Scientific and Statistical Computing, vol.7, issue.2, pp.639-659, 1986.
DOI : 10.1137/0907043

S. Poles and A. Lovison, A polynomial chaos approach to robust multiobjective optimization, in: Dagstuhl Semin, Proc, 2009.

P. Feliot, Y. Le-guennec, J. Bect, and E. Vazquez, Design of a commercial aircraft environment control system using Bayesian optimization techniques, EngOpt 2016 -5th Int. Conf. Eng. Optim, pp.19-23, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01377722

M. Han and P. Kopacek, Optimization using Artificial Neural Networks, IFAC Proceedings Volumes, vol.28, issue.24, pp.357-360, 1995.
DOI : 10.1016/S1474-6670(17)46576-1

R. F. Gunst, Response Surface Methodology: Process and Product Optimization Using Designed Experiments, Technometrics, vol.38, issue.3, pp.284-286, 1996.
DOI : 10.1080/00401706.1996.10484509

R. Benassi, J. Bect, and E. Vazquez, Bayesian Optimization Using Sequential Monte Carlo, Learn. Intell
DOI : 10.1007/978-3-642-34413-8_24
URL : https://hal.archives-ouvertes.fr/hal-00717195

M. Moustapha, B. Sudret, J. Bourinet, and B. Guillaume, Metamodeling for Crashworthiness Design : Comparative Study of Kriging and Support Vector Regression, Uncertainties 2014 -Proc. 2nd Int, 2014.

M. Billaud-friess, A. Nouy, and O. Zahm, A tensor approximation method based on ideal minimal residual formulations for the solution of high-dimensional problems, ESAIM: Mathematical Modelling and Numerical Analysis, vol.48, issue.6, pp.1777-1806, 2014.
DOI : 10.1017/CBO9780511762291
URL : https://hal.archives-ouvertes.fr/hal-00861914

M. Haardt, F. Roemer, and G. D. Galdo, Higher-Order SVD-Based Subspace Estimation to Improve the Parameter Estimation Accuracy in Multidimensional Harmonic Retrieval Problems, IEEE Transactions on Signal Processing, vol.56, issue.7, pp.3198-3213, 2008.
DOI : 10.1109/TSP.2008.917929

I. Oseledets and E. Tyrtyshnikov, TT-cross approximation for multidimensional arrays, Linear Algebra and its Applications, vol.432, issue.1, pp.70-88, 2010.
DOI : 10.1016/j.laa.2009.07.024
URL : https://doi.org/10.1016/j.laa.2009.07.024

S. Wang and Z. Zhang, Improving CUR Matrix Decomposition and the Nystrom Approximation via Adaptive Sampling, J. Mach. Learn. Res, vol.14, pp.2729-2769, 2013.

D. Amsallem, J. Cortial, and C. Farhat, Towards Real-Time Computational-Fluid-Dynamics-Based Aeroelastic Computations Using a Database of Reduced-Order Information, AIAA Journal, vol.2009, issue.9, pp.2029-2037, 2010.
DOI : 10.2514/6.2009-800

P. Benner, S. Gugercin, and K. Willcox, A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems, SIAM Review, vol.57, issue.4, pp.483-531, 2015.
DOI : 10.1137/130932715

M. W. Mahoney and P. Drineas, CUR matrix decompositions for improved data analysis, Proc. Natl. Acad. Sci, pp.697-702, 2009.
DOI : 10.1073/pnas.0500191102
URL : http://www.pnas.org/content/106/3/697.full.pdf

N. Mitrovic, M. T. Asif, U. Rasheed, J. Dauwels, and P. Jaillet, CUR decomposition for compression and compressed sensing of large-scale traffic data, 16th International IEEE Conference on Intelligent Transportation Systems (ITSC 2013), pp.1475-1480, 2013.
DOI : 10.1109/ITSC.2013.6728438

D. C. Sorensen, M. Embree, A. Deim-induced, and C. Factorization, A DEIM Induced CUR Factorization, SIAM Journal on Scientific Computing, vol.38, issue.3, pp.1454-1482, 2016.
DOI : 10.1137/140978430
URL : http://arxiv.org/pdf/1407.5516

J. Macqueen, Some methods for classification and analysis of multivariate observations, Proc. 5th Berkeley Symp, pp.281-297, 1967.

H. Kriegel, P. Kr{-"-{o}ger, and A. Zimek, Clustering high-dimensional data, ACM Transactions on Knowledge Discovery from Data, vol.3, issue.1, pp.1-58, 2009.
DOI : 10.1145/1497577.1497578

A. Nouy, Low-Rank Tensor Methods for Model Order Reduction, Handb. Uncertain. Quantif, pp.1-26
DOI : 10.1007/978-3-319-12385-1_21
URL : https://hal.archives-ouvertes.fr/hal-01262403

E. J. Candes and T. Tao, The Dantzig selector: Statistical estimation when p is much larger than n, The Annals of Statistics, vol.35, issue.6, pp.2313-2351, 2007.
DOI : 10.1214/009053606000001523
URL : http://doi.org/10.1214/009053606000001523

J. S. Hesthaven and S. Ubbiali, Non-intrusive reduced order modeling of nonlinear problems using neural networks, Journal of Computational Physics, 2017.
DOI : 10.1016/j.jcp.2018.02.037

D. Xiao, F. Fang, C. C. Pain, and I. M. Navon, A parameterized non-intrusive reduced order model and error analysis for general time-dependent nonlinear partial differential equations and its applications, Computer Methods in Applied Mechanics and Engineering, vol.317, pp.868-889, 2017.
DOI : 10.1016/j.cma.2016.12.033

M. Charrier, Y. Tourbier, L. Jézéquel, and O. Dessombz, Strategic decision support through combinatorial optimization with costly evaluation function, Nafems World Congr. Procedings, 2017.

. Acknowledgements, This research work has been carried out in the framework of IRT SystemX, Paris-Saclay, France, and therefore granted with public funds within the scope of the French Program