R. Ghanem and P. Spanos, Stochastic Finite Elements: A Spectral Approach, 1991.

C. Soize and R. Ghanem, Physical systems with random uncertainties: Chaos representations with arbitrary probability measure, SIAM Journal of Scientific Computing, vol.26, issue.2, pp.395-410, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00686211

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

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

R. Ghanem, C. Soize, and C. Thimmisetty, Optimal well-placement using a probabilistic learning, Data-Enabled Discovery and Applications, vol.2, issue.1, pp.1-16, 2018.

C. Soize, Uncertainty Quantification. An Accelerated Course with Advanced Applications in Computational Engineering, 2017.
URL : https://hal.archives-ouvertes.fr/hal-00826082

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.

C. Soize, Polynomial chaos expansion of a multimodal random vector, SIAM/ASA Journal on Uncertainty Quantification, vol.3, issue.1, pp.34-60, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01105959

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-01325279

D. J. Dolvin, 15th AIAA International Space Planes and Hypersonic Systems and Technologies Conference, 2008.

D. J. Dolvin, Hypersonic International Flight Research and Experimentation, p.16

, 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, 45th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, 2009.

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

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, Tech. rep, 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, 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, 2006.

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, issue.2, pp.1603-1611, 2015.

G. Lacaze, Z. P. Vane, and J. C. Oefelein, Large Eddy Simulation of the HIFiRE Direct Connect Rig Scramjet Combustor, 55th AIAA Aerospace Sciences Meeting, 2017.

M. Germano, U. Piomelli, P. Moin, and W. Cabot, A dynamic subgrid-scale eddy viscosity model, Physics of Fluids, vol.3, issue.7, pp.1760-1765, 1991.

B. Vreman, B. Geurts, and H. Kuerten, On the formulation of the dynamic mixed subgrid-scale model, Physics of Fluids, vol.6, issue.12, pp.4057-4059, 1994.

M. R. Gruber, K. Jackson, and J. Liu, Hydrocarbon-Fueled Scramjet Combustor Flowpath Development for Mach 6-8 HIFiRE Flight Experiments, Tech. rep, 2008.

R. Coifman and S. Lafon, Diffusion maps, applied and computational harmonic analysis, Applied and Computational Harmonic Analysis, vol.21, issue.1, pp.5-30, 2006.

R. Coifman, I. Kevrekidis, S. Lafon, M. Maggioni, and B. Nadler, Diffusion maps, reduction coordinates, and low dimensional representation of stochastic systems, SIAM J. Multiscale Model. Simul, vol.7, issue.2, pp.842-864, 2008.

M. Belkin and P. Niyogi, Laplacian eigenmaps for dimensionality reduction and data representation, Neural Cmoputation, vol.15, pp.1373-1396, 2003.

C. Soize, R. G. Ghanem, C. Safta, X. Huan, Z. P. Vane et al., Entropy-based closure for probabilistic learning on manifolds, Journal of Computational Physics, vol.388, pp.528-533, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02100250

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

K. Burrage, I. Lenane, and G. Lythe, Numerical methods for second-order stochastic differential equations, SIAM Journal on Scientific Computing, vol.29, issue.1, pp.245-264, 2007.

L. Scrucca, GA: A package for genetic algorithms in R, Journal of Statistical Software, vol.53, issue.4, pp.1-37, 2013.

. R-core-team, R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, 2018.