Polar Gaussian Processes and Experimental Designs in Circular Domains

Espéran Padonou (1, 2, 3, 4) , Olivier Roustant (1, 5, 2, 3, 4)

1 DEMO-ENSMSE - Département Décision en Entreprise : Modélisation, Optimisation
2 Mines Saint-Étienne MSE - École des Mines de Saint-Étienne
3 LIMOS - Laboratoire d'Informatique, de Modélisation et d'Optimisation des Systèmes
4 FAYOL-ENSMSE - Institut Henri Fayol
5 GdR MASCOT-NUM - Méthodes d'Analyse Stochastique des Codes et Traitements Numériques

Predicting on circular domains is a central issue that can be addressed by Gaussian process (GP) regression. However, usual GP models do not take into account the geometry of the disk in their covariance structure (or kernel), which may be a drawback at least for industrial processes involving a rotation or a diffusion from the center of the disk. We introduce so-called polar GPs defined on the space of polar coordinates. Their kernels are obtained as a combination of a kernel for the radius and a kernel for the angle, based on either chordal or geodesic distances on the circle. Their efficiency is illustrated on two industrial applications. We further consider the problem of designing experiments on the disk. Two new Latin hypercube designs are obtained, by defining a valid maximin criterion for polar coordinates. Finally, an extension of the whole methodology to higher dimensions is investigated. Read More: http://epubs.siam.org/doi/abs/10.1137/15M1032740

Domaines: Modélisation et simulation

Espéran Padonou, Olivier Roustant. Polar Gaussian Processes and Experimental Designs in Circular Domains. SIAM/ASA Journal on Uncertainty Quantification, 2016, 4 (1), pp.1014 - 1033. ⟨10.1137/15M1032740⟩. ⟨emse-01412189⟩