, A is unknown, non hyper-rectangular

D. References-i-allard, R. Senoussi, and E. Porcu, , 2016.

, Anisotropy models for spatial data, Mathematical Geosciences, vol.48, issue.3, pp.305-328

D. Gaudrie, R. L. Riche, V. Picheny, B. Enaux, and V. Herbert, , 2019.

, Modeling and optimization with gaussian processes in reduced eigenbases-extended version

D. R. Jones, M. Schonlau, and W. J. Welch, , 1998.

, Efficient Global Optimization of expensive black-box functions, Journal of Global optimization, vol.13, issue.4, pp.455-492

B. Raghavan, P. Breitkopf, Y. Tourbier, and P. Villon, , 2013.

, Towards a space reduction approach for efficient structural shape optimization. Structural and Multidisciplinary Optimization, vol.48, pp.987-1000

B. Raghavan, G. Le-quilliec, P. Breitkopf, A. Rassineux, J. Roelandt et al., , 2014.

, Numerical assessment of springback for the deep drawing process by level set interpolation using shape manifolds, International journal of material forming, vol.7, issue.4, pp.487-501

M. B. Stegmann and D. D. Gomez, , 2002.

, A brief introduction to statistical shape analysis. Informatics and mathematical modelling, DTU, issue.11, p.15

Z. Wang, M. Zoghi, F. Hutter, D. Matheson, D. Freitas et al., , 2013.

, Bayesian optimization in high dimensions via random embeddings, Twenty-Third International Joint Conference on Artificial Intelligence

G. Yi, J. Shi, and T. Choi, , 2011.

, Penalized Gaussian process regression and classification for high-dimensional nonlinear data, Biometrics, vol.67, issue.4, pp.1285-1294

R. Standard and . Wang, Embedding matrix a ? R D×d with d e ? d D, entries of x ? [?1, 1] D . ? N (0, ? j ): random line which takes the structure of ? ? ? a into account. Intrinsic dimensionality Meta-modeling in eigenbasis Optimization in eigenbasis Conclusions What about PLS? Output-related dimension reduction, 2013.

, Linear method Only n eigenshapes (shape reconstruction error)

.. .. ·), Y m (·) have to share the same input space (? ? ? space) for the maximization of EI's multi-objective pendant