Y. Lecun, L. Bottou, Y. Bengio, and P. Haffner, Gradient-based learning applied to document recognition, Proceedings of the IEEE, vol.86, issue.11, pp.2278-2324, 1998.
DOI : 10.1109/5.726791

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

J. Spall, Introduction to Stochastic Search and Optimization, 2003.
DOI : 10.1002/0471722138

A. Konak, D. Coit, and A. Smith, Multi-objective optimization using genetic algorithms: A tutorial, Reliability Engineering & System Safety, vol.91, issue.9, pp.992-1007, 2006.
DOI : 10.1016/j.ress.2005.11.018

URL : http://citeseerx.ist.psu.edu/viewdoc/download?doi=

C. Coello and C. A. , Evolutionary multi-objective optimization: a historical view of the field, IEEE Computational Intelligence Magazine, vol.1, issue.1, pp.28-36, 2006.
DOI : 10.1109/MCI.2006.1597059

D. Jones, M. Schonlau, and W. Welch, Efficient global optimization of expensive black-box functions, Journal of Global Optimization, vol.13, issue.4, pp.455-492, 1998.
DOI : 10.1023/A:1008306431147

N. Queipo, R. Haftka, W. Shyy, T. Goel, R. Vaidyanathan et al., Surrogate-based analysis and optimization, Progress in Aerospace Sciences, vol.41, issue.1, pp.1-28, 2005.
DOI : 10.1016/j.paerosci.2005.02.001

R. Byrd, G. Chin, W. Neveitt, and J. Nocedal, On the Use of Stochastic Hessian Information in Optimization Methods for Machine Learning, SIAM Journal on Optimization, vol.21, issue.3, pp.977-995, 2011.
DOI : 10.1137/10079923X

T. Homem-de-mello and G. Bayraksan, Monte Carlo sampling-based methods for stochastic optimization, Surveys in Operations Research and Management Science, vol.19, issue.1, pp.56-85, 2014.
DOI : 10.1016/j.sorms.2014.05.001

J. Kleijnen, W. Van-beers, and I. Van-nieuwenhuyse, Constrained optimization in expensive simulation: Novel approach, European Journal of Operational Research, vol.202, issue.1, pp.164-174, 2010.
DOI : 10.1016/j.ejor.2009.05.002

Y. Sui, A. Gotovos, J. Burdick, and A. Krause, Safe exploration for optimization with gaussian processes, Proceedings of the 32 nd International Conference on Machine Learning, 2015.

Z. Wang, M. Zoghi, F. Hutter, D. Matheson, and N. De-freitas, Bayesian optimization in a billion dimensions via random embeddings, Journal of Artificial Intelligence Research, vol.55, pp.361-387, 2016.

J. Xie, P. Frazier, and S. Chick, Bayesian Optimization via Simulation with Pairwise Sampling and Correlated Prior Beliefs, Operations Research, vol.64, issue.2, pp.542-559, 2016.
DOI : 10.1287/opre.2016.1480

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

R. Ghanem and P. Spanos, Stochastic Finite Elements: A Spectral Approach, 1991.
DOI : 10.1007/978-1-4612-3094-6

C. Soize, A nonparametric model of random uncertainties for reduced matrix models in structural dynamics, Probabilistic Engineering Mechanics, vol.15, issue.3, pp.277-294, 2000.
DOI : 10.1016/S0266-8920(99)00028-4

URL : https://hal.archives-ouvertes.fr/hal-00686293

C. Soize and R. Ghanem, Physical Systems with Random Uncertainties: Chaos Representations with Arbitrary Probability Measure, SIAM Journal on Scientific Computing, vol.26, issue.2, pp.395-410, 2004.
DOI : 10.1137/S1064827503424505

URL : https://hal.archives-ouvertes.fr/hal-00686211

R. Ghanem, D. Higdon, and H. Owhadi, Handbook of Uncertainty Quantification, 2017.

X. Du and W. Chen, Sequential Optimization and Reliability Assessment Method for Efficient Probabilistic Design, Journal of Mechanical Design, vol.126, issue.2, pp.225-233, 2004.
DOI : 10.1115/1.1649968

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

W. Yao, X. Chen, W. Luo, M. Guo, and J. , Review of uncertainty-based multidisciplinary design optimization methods for aerospace vehicles, Progress in Aerospace Sciences, vol.47, issue.6, pp.450-479, 2011.
DOI : 10.1016/j.paerosci.2011.05.001

M. Eldred, DESIGN UNDER UNCERTAINTY EMPLOYING STOCHASTIC EXPANSION METHODS, International Journal for Uncertainty Quantification, vol.1, issue.2, pp.119-146, 2011.
DOI : 10.1615/IntJUncertaintyQuantification.v1.i2.20

R. Coifman, S. Lafon, A. Lee, M. Maggioni, B. Nadler et al., Geometric diffusions as a tool for harmonic analysis and structure definition of data: Diffusion maps, Proceedings of the National Academy of Sciences, vol.102, issue.21, pp.7426-7431, 2005.
DOI : 10.1073/pnas.0500896102

R. Coifman and S. Lafon, Diffusion maps, Applied and Computational Harmonic Analysis, vol.21, issue.1, pp.5-30, 2006.
DOI : 10.1016/j.acha.2006.04.006

R. Talmon and R. Coifman, Intrinsic modeling of stochastic dynamical systems using empirical geometry, Applied and Computational Harmonic Analysis, vol.39, issue.1, pp.138-160, 2015.
DOI : 10.1016/j.acha.2014.08.006

C. Soize, Construction of probability distributions in high dimension using the maximum entropy principle: Applications to stochastic processes, random fields and random matrices, International Journal for Numerical Methods in Engineering, vol.195, issue.4, pp.1583-1611, 2008.
DOI : 10.1007/978-3-662-12616-5

URL : https://hal.archives-ouvertes.fr/hal-00684517

R. Neal and . Mcmc-using-hamiltonian-dynamics, Handbook of Markov Chain Monte Carlo, 2010.

M. Girolami and B. Calderhead, Riemann manifold Langevin and Hamiltonian Monte Carlo methods, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.13, issue.10, pp.123-214, 2011.
DOI : 10.1162/08997660460734047

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

J. Kaipio and E. Somersalo, Statistical and Computational Inverse Problems, 2005.

C. Robert and G. Casella, Monte Carlo Statistical Methods, 2005.

C. Soize and R. Ghanem, Data-driven probability concentration and sampling on manifold, Journal of Computational Physics, vol.321, pp.242-258, 2016.
DOI : 10.1016/j.jcp.2016.05.044

URL : https://hal.archives-ouvertes.fr/hal-01283842

A. Bowman and A. Azzalini, Applied Smoothing Techniques for Data Analysis, 1997.

D. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization, 2015.
DOI : 10.1002/9781118575574

H. Rosenbrock, An Automatic Method for Finding the Greatest or Least Value of a Function, The Computer Journal, vol.3, issue.3, pp.175-184, 1960.
DOI : 10.1093/comjnl/3.3.175

B. Adams, L. Bauman, W. Bohnhoff, K. Dalbey, M. Ebeida et al., Dakota, a multilevel parallel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis: Version 6.0 users manual, p.2015
DOI : 10.2172/1177077