Grassmannian kriging with applications in pod-based model order reduction

. In this work, we propose a generalization of the kriging interpolation procedure from Euclidean spaces to Grassmann manifolds in the context of model order reduction based on Proper Orthogonal Decomposition (POD). This generalization relies on the introduction of a so-called geodesic experimental semi-variogram which depends solely on the repartition of the interpolation values on the manifold. Here, the interpolation values are the subspaces engendered by the bases obtained by POD of the solutions associated with sampling parameters. Three CFD applications are presented: (i) the two-dimensional flow pas a cylinder in a channel, (ii) the two-dimensional Burger equation and (iii) the one dimensional wave equation. For each application, the proposed method to compute the interpolated basis associated with a given parameter proves faster than state-of-the-art method while achieving the same accuracy.