J. Rohmer and D. Idier, A meta-modelling strategy to identify the critical offshore conditions for coastal flooding. Natural Hazards and Earth System Sciences, vol.12, pp.2943-2955, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00733495

G. Jia and A. A. Taflanidis, Kriging metamodeling for approximation of highdimensional wave and surge responses in real-time storm/hurricane risk assessment, Computer Methods in Applied Mechanics and Engineering, vol.261, pp.24-38, 2013.

A. Rueda, B. Gouldby, F. Méndez, A. Tomás, I. Losada et al., The use of wave propagation and reduced complexity inundation models and metamodels for coastal flood risk assessment, Journal of Flood Risk Management, vol.9, issue.4, pp.390-401, 2016.

T. Muehlenstaedt, J. Fruth, and O. Roustant, Computer experiments with functional inputs and scalar outputs by a norm-based approach, Statistics and Computing, vol.27, issue.4, pp.1083-1097, 2017.
URL : https://hal.archives-ouvertes.fr/emse-01072023

S. Nanty, C. Helbert, A. Marrel, N. Pérot, and C. Prieur, Sampling, metamodeling, and sensitivity analysis of numerical simulators with functional stochastic inputs, SIAM/ASA Journal on Uncertainty Quantification, vol.4, issue.1, pp.636-659, 2016.

A. Forrester, A. Sobester, and A. Keane, Engineering design via surrogate modelling: a practical guide, 2008.

T. J. Santner, B. J. Williams, W. Notz, and B. J. Williams, The design and analysis of computer experiments, vol.1, 2003.

C. Lataniotis, S. Marelli, and B. Sudret, The Gaussian process modelling module in UQLab, Soft Computing in Civil Engineering, vol.2, issue.3, pp.91-116, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01901966

J. O. Ramsay and B. W. Silverman, Applied functional data analysis: methods and case studies, 2007.

A. Marrel, B. Iooss, M. Jullien, B. Laurent, and E. Volkova, Global sensitivity analysis for models with spatially dependent outputs, Environmetrics, vol.22, issue.3, pp.383-397, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00430171

C. V. Mai and B. Sudret, Surrogate models for oscillatory systems using sparse polynomial chaos expansions and stochastic time warping, SIAM/ASA Journal on Uncertainty Quantification, vol.5, issue.1, pp.540-571, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01421106

P. Vincent, H. Larochelle, Y. Bengio, and P. A. Manzagol, Extracting and composing robust features with denoising autoencoders, Proceedings of the 25th international conference on Machine learning, pp.1096-1103, 2008.

P. T. Reiss, J. Goldsmith, H. L. Shang, and R. T. Ogden, Methods for scalar-onfunction regression, International Statistical Review, vol.85, issue.2, pp.228-249, 2017.

A. Antoniadis, C. Helbert, C. Prieur, and L. Viry, Spatio-temporal metamodeling for West African monsoon, Environmetrics, vol.23, issue.1, pp.24-36, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00551303

J. Rohmer, Boosting kernel-based dimension reduction for jointly propagating spatial variability and parameter uncertainty in long-running flow simulators, Mathematical Geosciences, vol.47, issue.2, pp.227-246, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01104564

P. G. Constantine, Active subspaces: Emerging ideas for dimension reduction in parameter studies, vol.2, 2015.

G. E. Hinton and R. R. Salakhutdinov, Reducing the dimensionality of data with neural networks, science, vol.313, issue.5786, pp.504-507, 2006.

A. Damianou and N. Lawrence, Deep gaussian processes. In: Artificial Intelligence and Statistics, pp.207-215, 2013.

W. Huang, D. Zhao, F. Sun, H. Liu, and C. E. , Scalable gaussian process regression using deep neural networks, Twenty-Fourth International Joint Conference on Artificial Intelligence, pp.3576-3582, 2015.

R. Calandra, J. Peters, C. E. Rasmussen, and M. P. Deisenroth, Manifold Gaussian processes for regression, 2016 International Joint Conference on Neural Networks (IJCNN), pp.3338-3345, 2016.

M. Fornasier, K. Schnass, and J. Vybiral, Learning functions of few arbitrary linear parameters in high dimensions, Foundations of Computational Mathematics, vol.12, issue.2, pp.229-262, 2012.

C. Lataniotis, S. Marelli, and B. Sudret, Extending classical surrogate modelling to ultrahigh dimensional problems through supervised dimensionality reduction: a data-driven approach, 2019.
URL : https://hal.archives-ouvertes.fr/hal-01959179

J. Sacks, W. J. Welch, T. J. Mitchell, and H. P. Wynn, Design and analysis of computer experiments, Statistical science, vol.4, pp.409-423, 1989.

J. Oakley and A. O'hagan, Bayesian inference for the uncertainty distribution of computer model outputs, Biometrika, vol.89, issue.4, pp.769-784, 2002.

C. E. Rasmussen, Gaussian processes in machine learning, In: Summer School on Machine Learning, pp.63-71, 2003.

M. L. Stein, Interpolation of spatial data: some theory for kriging, 2012.

. Anr-riscope-project, Accessed, pp.2018-2030

N. Booij, L. Holthuijsen, and R. R. The, SWAN" wave model for shallow water, In: Coastal Engineering, pp.668-676, 1996.

J. Van-der-meer, N. Allsop, T. Bruce, D. Rouck, J. Kortenhaus et al., EurOtop: Manual on wave overtopping of sea defences and related sturctures: an overtopping manual largely based on European research, but for worlwide application, 2016.

D. Idier, J. Rohmer, R. Pedreros, L. Roy, S. Lambert et al., Coastal flood: a composite method for past events characterisation providing insights in past, present and future hazards, AGU Fall Meeting, 2019.

M. Moustapha, B. Sudret, J. M. Bourinet, and B. Guillaume, Quantile-based optimization under uncertainties using adaptive Kriging surrogate models. Structural and multidisciplinary optimization, vol.54, pp.1403-1421, 2016.

P. Abrahamsen, A review of Gaussian random fields and correlation functions, Norsk Regnesentral/Norwegian Computing Center Oslo, 1997.

D. Ginsbourger, B. Rosspopoff, G. Pirot, N. Durrande, and R. P. , Distancebased kriging relying on proxy simulations for inverse conditioning. Advances in water resources, vol.52, pp.275-291, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00698582

H. G. Pulido, . De-la-vara, R. Salazar, P. G. González, C. T. Martínez et al., Análisis y diseño de experimentos, 2012.

D. C. Montgomery, Design and analysis of experiments, 2017.

J. Friedman, T. Hastie, and R. Tibshirani, The elements of statistical learning, vol.1, 2001.

B. D. Ripley, Spatial statistics, vol.575, 2005.

F. Bachoc, Cross validation and maximum likelihood estimations of hyperparameters of Gaussian processes with model misspecification, Computational Statistics & Data Analysis, vol.66, pp.55-69, 2013.

J. Green, J. L. Whalley, and C. G. Johnson, Automatic programming with ant colony optimization, Proceedings of the 2004 UK Workshop on Computational Intelligence, pp.70-77, 2004.

D. Karaboga, C. Ozturk, N. Karaboga, and B. Gorkemli, Artificial bee colony programming for symbolic regression, Information Sciences, vol.209, pp.1-15, 2012.

N. Q. Uy, N. X. Hoai, M. O'neill, R. I. Mckay, and E. Galván-lópez, Semanticallybased crossover in genetic programming: application to real-valued symbolic regression. Genetic Programming and Evolvable Machines, vol.12, pp.91-119, 2011.

H. Maatouk and X. Bay, A new rejection sampling method for truncated multivariate Gaussian random variables restricted to convex sets. In: Monte carlo and quasi-monte carlo methods, pp.521-530, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01063978

A. F. López-lopera, F. Bachoc, N. Durrande, and O. Roustant, Finite-dimensional Gaussian approximation with linear inequality constraints, SIAM/ASA Journal on Uncertainty Quantification, vol.6, issue.3, pp.1224-1255, 2018.

J. Rougier, Efficient emulators for multivariate deterministic functions, Journal of Computational and Graphical Statistics, vol.17, issue.4, pp.827-843, 2008.

A. Marrel, B. Iooss, D. Veiga, S. Ribatet, and M. , Global sensitivity analysis of stochastic computer models with joint metamodels. Statistics and Computing, vol.22, pp.833-847, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00232805

V. Picheny, D. Ginsbourger, Y. Richet, and G. Caplin, Quantile-based optimization of noisy computer experiments with tunable precision, Technometrics, vol.55, issue.1, pp.2-13, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00578550

V. Moutoussamy, S. Nanty, and B. Pauwels, Emulators for stochastic simulation codes, ESAIM: Proceedings and Surveys, vol.48, pp.116-155, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01011770

T. Browne, B. Iooss, L. L. Gratiet, J. Lonchampt, and R. E. , Stochastic simulators based optimization by Gaussian process metamodels -application to maintenance investments planning issues. Quality and Reliability Engineering International, vol.32, pp.2067-2080, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01198463

M. D. Mckay, R. J. Beckman, and W. J. Conover, Comparison of three methods for selecting values of input variables in the analysis of output from a computer code, Technometrics, vol.21, issue.2, pp.239-245, 1979.

D. Boor and C. , A Practical Guide to Splines, Applied mathematical sciences, vol.27, pp.15-16, 1978.

S. Nanty, C. Helbert, A. Marrel, N. Pérot, and C. Prieur, Uncertainty quantification for functional dependent random variables, Computational Statistics, vol.32, issue.2, pp.559-583, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01075840

I. Jolliffe, Principal component analysis, 2011.

I. Papaioannou, M. Ehre, and D. Straub, PLS-based adaptation for efficient PCE representation in high dimensions, Journal of Computational Physics, vol.387, pp.186-204, 2019.

A. Marrel, B. Iooss, F. Van-dorpe, and E. Volkova, An efficient methodology for modeling complex computer codes with Gaussian processes, Computational Statistics & Data Analysis, vol.52, issue.10, pp.4731-4744, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00239492

O. Roustant, D. Ginsbourger, Y. Deville, and . Dicekriging, Diceoptim: Two R packages for the analysis of computer experiments by kriging-based metamodelling and optimization, Journal of Statistical Software, vol.51, issue.1, p.54, 2012.
URL : https://hal.archives-ouvertes.fr/emse-00741762

J. Nilsson, S. De-jong, and A. K. Smilde, Multiway calibration in 3D QSAR, Journal of Chemometrics: A Journal of the Chemometrics Society, vol.11, issue.6, pp.511-524, 1997.

Z. Shen, K. C. Toh, and S. Yun, An accelerated proximal gradient algorithm for frame-based image restoration via the balanced approach, SIAM Journal on Imaging Sciences, vol.4, issue.2, pp.573-596, 2011.

E. Taillard, Some efficient heuristic methods for the flow shop sequencing problem, European journal of Operational research, vol.47, issue.1, pp.65-74, 1990.

S. Marque-pucheu, Gaussian process regression of two nested computer codes, 2018.
URL : https://hal.archives-ouvertes.fr/tel-02092072

S. Marque-pucheu, G. Perrin, and J. Garnier, Efficient sequential experimental design for surrogate modeling of nested codes, ESAIM: Probability and Statistics, vol.23, pp.245-270, 2019.
URL : https://hal.archives-ouvertes.fr/hal-01657827

B. E. Dixit and . Essentials, , 2016.

W. Hendrickx, D. Gorissen, and T. Dhaene, Grid enabled sequential design and adaptive metamodeling, Proceedings of the 2006 Winter Simulation Conference, pp.872-881, 2006.

W. Hendrickx and T. Dhaene, Sequential design and rational metamodelling, Proceedings of the 2005 Winter Simulation Conference, pp.290-298, 2005.

L. Davis, Handbook of genetic algorithms. CUMINCAD, 1991.

M. Dorigo and M. Birattari, Ant colony optimization, 2010.

U. Mori, A. Mendiburu, and J. A. Lozano, Distance measures for time series in R: The TSdist package, R journal, vol.8, issue.2, pp.451-459, 2016.

J. Bigot, R. Gouet, T. Klein, and A. López, Geodesic PCA in the Wasserstein space by convex PCA, Annales de l'Institut Henri Poincaré, vol.53, pp.1-26, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01978864

L. Carrere, F. Lyard, M. Cancet, A. Guillot, and N. Picot, a new tidal model-Validation results and perspectives for improvements, Proceedings of the ESA living planet symposium, pp.9-13, 2014.

G. Compo, J. Whitaker, P. Sardeshmukh, N. Matsui, R. Allan et al.,

. Noaa/cires, Twentieth Century Global Reanalysis Version 2c. Research Data Archive at the National Center for Atmospheric Research

, , 2015.

D. Dee, M. Balmaseda, G. Balsamo, R. Engelen, A. Simmons et al., Toward a consistent reanalysis of the climate system, Bulletin of the American Meteorological Society, vol.95, issue.8, pp.1235-1248, 2014.

H. Muller, L. Pineau-guillou, D. Idier, and F. Ardhuin, Atmospheric storm surge modeling methodology along the French, Atlantic and English Channel) coast. Ocean Dynamics, vol.64, issue.11, pp.1671-1692, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01076991

X. Bertin, E. Prouteau, and C. Letetrel, A significant increase in wave height in the North Atlantic Ocean over the 20th century, Global and Planetary Change, vol.106, pp.77-83, 2013.

E. Charles, D. Idier, J. Thiébot, L. Cozannet, G. Pedreros et al., Wave climate variability and trends in the Bay of Biscay from 1958 to, Journal of Climate, vol.25, pp.2020-2039, 2001.
URL : https://hal.archives-ouvertes.fr/hal-00647448

E. Boudière, C. Maisondieu, F. Ardhuin, M. Accensi, L. Pineau-guillou et al., A suitable metocean hindcast database for the design of Marine energy converters, International Journal of Marine Energy, vol.3, pp.40-52, 2013.

D. P. Bertsekas, Nonlinear programming, Journal of the Operational Research Society, vol.48, issue.3, pp.334-334, 1997.

T. Hs,

B. Bobwa,

, Homere Ifremer and LOPS, vol.74

, Iowaga/Norgasug Ifremer and LOPS, vol.74

A. Table, 6: Sources of data for the coastal flooding application case