. For-?-=-1, S. Aanonsen, A. Eide, L. Holden, and J. Aasen, ? sim , compute ( w ? References 1 Optimizing reservoir performance under uncertainty with application to well location, SPE annual technical conference and exhibition, pp.67-76, 1995.

V. Artus, L. Durlofsky, J. Onwunala, and K. Aziz, Optimization of nonconventional wells under uncertainty using statistical proxies, Computational Geosciences, vol.10, issue.4, pp.389-404, 2006.
DOI : 10.1007/s10596-006-9031-9

M. Babaei, A. Alkhatib, and I. Pan, Robust optimization of subsurface flow using polynomial chaos and response surface surrogates, Computational Geosciences, vol.11, issue.10, pp.979-998, 2015.
DOI : 10.1007/s00500-006-0145-8

W. Bangerth, H. Klie, M. Wheeler, P. Stoffa, and M. Sen, On optimization algorithms for the reservoir oil well placement problem, Computational Geosciences, vol.8, issue.3, pp.303-319, 2006.
DOI : 10.2118/86880-PA

B. Beckner and X. Song, Field Development Planning Using Simulated Annealing - Optimal Economic Well Scheduling and Placement, SPE Annual Technical Conference and Exhibition, 1995.
DOI : 10.2118/30650-MS

M. Bellout, D. Echeverria-ciaurri, L. Durlofsky, B. Foss, and J. Kleppe, Joint optimization of oil well placement and controls, Computational Geosciences, vol.73, issue.3???4, pp.1061-1079, 2012.
DOI : 10.1016/j.petrol.2010.07.002

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

L. Christiansen, A. Capolei, and J. Jrgensen, Time-explicit methods for joint economical and geological risk mitigation in production optimization, Journal of Petroleum Science and Engineering, vol.146, pp.158-169, 2016.
DOI : 10.1016/j.petrol.2016.04.018

M. Christie and M. Blunt, Tenth spe comparative solution project: a comparison of upscaling techniques, SPE Reservoir Evaluation & Engineering, vol.4, 2001.

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. 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

G. Van-essen, M. Zandvilet, P. V. Den-hof, O. Bosgra, and J. Jansen, Robust Waterflooding Optimization of Multiple Geological Scenarios, SPE Journal, vol.14, issue.01, pp.202-210, 2009.
DOI : 10.2118/102913-PA

R. Ghanem, Scales of fluctuation and the propagation of uncertainty in random porous media, Water Resources Research, vol.60, issue.9, pp.2123-2136, 1998.
DOI : 10.2307/2371268

R. Ghanem and C. Soize, Probabilistic non-convex constrained optimization with fixed number of function evaluations, International Journal for Numerical Methods in Engineering, 2017.

B. Guyaguler and R. Horne, Uncertainty assessment of well placement optimization, SPE Reservoir Evaluation & Engineering, vol.7, issue.1, pp.23-32, 2004.

M. Jesmani, M. Bellout, R. Hanea, and B. Foss, Well placement optimization subject to realistic field development constraints, Computational Geosciences, vol.16, issue.2, pp.1185-1209, 2016.
DOI : 10.1007/s10596-011-9244-4

L. Li, B. Jafarpour, and M. Mohammad-khaninezhad, A simultaneous perturbation stochastic approximation algorithm for coupled well placement and control optimization under geologic uncertainty, Computational Geosciences, vol.8, issue.3, pp.167-188, 2013.
DOI : 10.2118/86880-PA

K. Rashid, W. Bailey, B. Couet, and D. Wilkinson, An Efficient Procedure for Expensive Reservoir-Simulation Optimization Under Uncertainty, SPE Economics & Management, vol.5, issue.04, pp.21-33, 2013.
DOI : 10.2118/167261-PA

D. Rian and A. Hage, Automatic Optimization of Well Locations in a North Sea Fractured Chalk Reservoir Using a Front Tracking Reservoir Simulator, International Petroleum Conference and Exhibition of Mexico, 1994.
DOI : 10.2118/28716-MS

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

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

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

J. Spall, Introduction to Stochastic Searh and Optimization, 2003.

W. Sun and L. Durlofsky, A New Data-Space Inversion Procedure for Efficient Uncertainty Quantification in Subsurface Flow Problems, Mathematical Geosciences, vol.19, issue.4, pp.679-715, 2017.
DOI : 10.1007/s10596-015-9483-x

C. Thimmisetty, P. Tsilifis, and R. Ghanem, Paper petroleum Artificial Intelligence for Engineering Design DOI Homogeneous chaos basis adaptation for design optimization under uncertainty: Application to the oil well placement problem, Analysis and Manufacturing, vol.31, issue.3, pp.265-276, 2017.

H. Wang, D. Echeverria-ciaurri, L. Durlofsky, and A. Cominelli, Optimal Well Placement Under Uncertainty Using a Retrospective Optimization Framework, SPE Journal, vol.17, issue.01, pp.112-121, 2012.
DOI : 10.2118/141950-PA

B. Yeten, L. Durlofsky, and K. Aziz, Optimization of nonconventional well type, location and trajectory, SPE annual technical conference and exhibition, 2002.

Y. Zhang, R. Lu, F. Forouzanfar, and A. Reynolds, Well placement and control optimization for WAG/SAG processes using ensemble-based method, Computers & Chemical Engineering, vol.101, pp.193-209, 2017.
DOI : 10.1016/j.compchemeng.2017.02.020