C. Soize and R. Ghanem, Data-driven probability concentration and sampling on manifold, Journal of Computational Physics, vol.321, pp.242-258, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01283842

G. C. Mantis and D. N. Mavris, A Bayesian Approach to Non-Deterministic Hypersonic Vehicle Design, SAE Aerospace Congress and Exhibition, 2001.

J. Witteveen, K. Duraisamy, and G. Iaccarino, Uncertainty Quantification and Error Estimation in Scramjet Simulation, 17th AIAA International Space Planes and Hypersonic Systems and Technologies Conference, 2011.

P. G. Constantine, M. Emory, J. Larsson, and G. Iaccarino, Exploiting active subspaces to quantify uncertainty in the numerical simulation of the HyShot II scramjet, Journal of Computational Physics, vol.302, pp.1-20, 2015.

G. Geraci, M. S. Eldred, and G. Iaccarino, A multifidelity multilevel Monte Carlo method for uncertainty propagation in aerospace applications, 19th AIAA Non-Deterministic Approaches Conference, 1951.

X. Huan, G. Geraci, C. Safta, M. S. Eldred, K. Sargsyan et al., Multifidelity Statistical Analysis of Large Eddy Simulations in Scramjet Computations, 20th AIAA Non-Deterministic Approaches Conference, 1180.

X. Huan, C. Safta, K. Sargsyan, G. Geraci, M. S. Eldred et al., Global Sensitivity Analysis and Estimation of Model Error, Toward Uncertainty Quantification in Scramjet Computations, AIAA Journal, vol.56, issue.3, pp.1170-1184, 2018.

M. Feil and S. Staudacher, Uncertainty quantification of a generic scramjet engine using a probabilistic collocation and a hybrid approach, CEAS Aeronautical Journal, 2018.

J. Urzay, Supersonic Combustion in Air-Breathing Propulsion Systems for Hypersonic Flight, Annual Review of Fluid Mechanics, vol.50, issue.1, pp.593-627, 2018.

R. Ghanem and C. Soize, Probabilistic nonconvex constrained optimization with fixed number of function evaluations, International Journal for Numerical Methods in Engineering, pp.1-25, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01576263

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, PNAS, vol.102, issue.21, pp.7426-7431, 2005.

V. Vapnik, The Nature of Statistical Learning Theory, 2000.

C. C. Aggarwal and C. Zhai, Mining Text Data, 2012.

A. S. Dalalyan and A. B. Tsybakov, Sparse regression learning by aggregation and Langevin Monte-Carlo, Journal of Computer and System Sciences, vol.78, issue.5, pp.1423-1443, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00773553

K. P. Murphy, Machine Learning: A Probabilistic Perspective, 2012.

M. F. Balcan and V. Feldman, Statistical active learning algorithms, Advances in Neural Information Processing Systems, pp.1295-1303, 2013.

G. James, D. Witten, T. Hastie, and R. Tibshirani, An Introduction to Statistical Learning, vol.112, 2013.

X. Dong, E. Gabrilovich, G. Heitz, W. Horn, N. Lao et al., Knowledge vault: A web-scale approach to probabilistic knowledge fusion, Proceedings of the 20th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp.601-610, 2014.

Z. Ghahramani, Probabilistic machine learning and artificial intelligence, Nature, vol.521, issue.7553, pp.452-459, 2015.

J. Taylor and R. J. Tibshirani, Statistical learning and selective inference, Proceedings of the National Academy of Sciences, vol.112, issue.25, pp.7629-7634, 2015.

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

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

N. Queipo, R. Haftka, W. Shyy, T. Goel, R. Vaidyanathan et al., Surrogate-based analysis and optimization, Progress in Aerospace Science, vol.41, issue.1, pp.1-28, 2005.

R. Byrd, G. Chin, W. Neveitt, and J. Nocedal, On the use of stochastic Hessian information in optimization methods for machine learning, SIAM Journal of Optimization, vol.21, issue.3, pp.977-995, 2011.

T. Homem-de-mello and G. Bayraksan, Monte Carlo sampling-based methods for stochastic optimization, Surveys in Operations Researh and Management Science, vol.19, issue.1, pp.56-85, 2014.

A. J. Keane, Statistical improvement criteria for use in multiobjective design optimization, AIAA Journal, vol.44, issue.4, pp.879-891, 2006.

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.

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 pair beliefs, Operations Research, vol.64, issue.2, pp.542-559, 2016.

X. Du, C. , and W. , Sequential optimization and reliability assessment method for efficient probabilistic design, ASME Journal of Mechanical Design, vol.126, issue.2, pp.225-233, 2004.

M. Eldred, Design under uncertainty employing stochastic expansion methods, International Journal for Uncertainty Quantification, vol.1, issue.2, pp.119-146, 2011.

W. Yao, X. Chen, W. Luo, M. Vantooren, and J. Guo, Review of uncertainty-based multidisciplinary design optimization methods for aerospace vehicles, Progress in Aerospace Sciences, vol.47, pp.450-479, 2011.

S. Kodiyalam and R. Gurumoorthy, Neural network approximator with novel learning scheme for design optimization with variable complexity data, AIAA Journal, vol.35, issue.4, pp.736-739, 1997.

H. Luo and S. Hanagud, Dynamic learning rate neural network training and composite structural damage detection, AIAA Journal, vol.35, issue.9, pp.1522-1527, 1997.

B. Tracey, D. Wolpert, A. , and J. J. , Using supervised learning to improve Monte Carlo integral estimation, AIAA Journal, vol.51, issue.8, pp.2015-2023, 2013.

A. P. Singh, S. Medida, and K. Duraisamy, Machine-learning-augmented predictive modeling of turbulent separated flows over airfoils, AIAA Journal, vol.55, issue.7, pp.2215-2227, 2017.

D. J. Dolvin, Hypersonic International Flight Research and Experimentation (HIFiRE), 15th AIAA International Space Planes and Hypersonic Systems and Technologies Conference, 2008.

D. J. Dolvin, Hypersonic International Flight Research and Experimentation, 16th AIAA/DLR/DGLR International Space Planes and Hypersonic Systems and Technologies Conference, 2009.

K. R. Jackson, M. R. Gruber, and T. F. Barhorst, The HIFiRE Flight 2 Experiment: An Overview and Status Update, p.45

, AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, AIAA Paper 2009-5029, 2009.

K. R. Jackson, M. R. Gruber, and S. Buccellato, HIFiRE Flight 2 Overview and Status Uptate, 17th AIAA International Space Planes and Hypersonic Systems and Technologies Conference, 2011.

K. R. Jackson, M. R. Gruber, and S. Buccellato, Mach 6-8+ Hydrocarbon-Fueled Scramjet Flight Experiment: The HIFiRE Flight 2 Project, Journal of Propulsion and Power, vol.31, issue.1, pp.36-53, 2015.

N. E. Hass, K. F. Cabell, and A. M. Storch, HIFiRE Direct-Connect Rig (HDCR) Phase I Ground Test Results from the NASA Langley Arc-Heated Scramjet Test Facility, 2010.

A. M. Storch, M. Bynum, J. Liu, and M. Gruber, Combustor Operability and Performance Verification for HIFiRE Flight 2, 17th AIAA International Space Planes and Hypersonic Systems and Technologies Conference, 2011.

K. F. Cabell, N. E. Hass, A. M. Storch, and M. Gruber, HIFiRE Direct-Connect Rig (HDCR) Phase I Scramjet Test Results from the NASA Langley Arc-Heated Scramjet Test Facility, 17th AIAA International Space Planes and Hypersonic Systems and Technologies Conference, 2011.

G. L. Pellett, S. N. Vaden, and L. G. Wilson, Opposed Jet Burner Extinction Limits: Simple Mixed Hydrocarbon Scramjet Fuels vs Air, 43rd AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, AIAA Paper, 2007.

T. Lu and C. K. Law, A directed relation graph method for mechanism reduction, Proceedings of the Combustion Institute, vol.30, issue.1, pp.1333-1341, 2005.

A. C. Zambon and H. K. Chelliah, Explicit reduced reaction models for ignition, flame propagation, and extinction of C2H4/CH4/H2 and air systems, Combustion and Flame, vol.150, issue.1-2, pp.71-91, 2007.

J. C. Oefelein, Large eddy simulation of turbulent combustion processes in propulsion and power systems, Progress in Aerospace Sciences, vol.42, issue.1, pp.2-37, 2006.

J. C. Oefelein, Simulation and analysis of turbulent multiphase combustion processes at high pressures, 1997.

J. C. Oefelein, R. W. Schefer, and R. S. Barlow, Toward validation of large eddy simulation for turbulent combustion, AIAA Journal, vol.44, issue.3, pp.418-433, 2006.

J. C. Oefelein, G. Lacaze, R. Dahms, A. Ruiz, and A. Misdariis, Effects of real-fluid thermodynamics on high-pressure fuel injection processes, SAE International Journal of Engines, vol.7, issue.3, pp.1125-1136, 2014.

G. Lacaze, A. Misdariis, A. Ruiz, and J. C. Oefelein, Analysis of high-pressure Diesel fuel injection processes using LES with real-fluid thermodynamics and transport, Proceedings of the Combustion Institute, vol.35, pp.1603-1611, 2015.

E. T. Jaynes, Information theory and statistical mechanics, Physical Review, vol.106, issue.4, pp.620-630, 1957.

E. T. Jaynes, Information Theory and Statistical Mechanics, Physical Review, vol.II, issue.2, pp.171-190, 1957.

M. R. Gruber, K. Jackson, and J. Liu, Hydrocarbon-fueled scramjet combustor flowpath development for Mach 6-8 HIFiRE flight experiments, 2008.

C. Soize, Polynomial chaos expansion of a multimodal random vector, SIAM/ASA Journal on Uncertainty Quantification, vol.3, issue.1, pp.34-60, 2015.
DOI : 10.1137/140968495

URL : https://hal.archives-ouvertes.fr/hal-01105959

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

D. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization, vol.2, 2015.

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.76, issue.10, pp.1583-1611, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00684517

M. Girolami and B. Calderhead, Riemann manifold Langevin and Hamiltonian Monte Carlo methods, Journal of the Royal Statistics Society, vol.73, issue.2, pp.123-214, 2011.
DOI : 10.1111/j.1467-9868.2010.00765.x

R. S. Neal, A. Brooks, G. Gelman, X. Jones, and . Meng, Handbook of Markov Chain Monte Carlo, 2012.

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

URL : https://onlinelibrary.wiley.com/doi/pdf/10.1002/0471722138.fmatter