Studying flows in random porous media leads to consider a permeability tensor which directly depends on the pore geometry. The latter can be characterised through the computation of various morphological parameters: Delaunay triangulation characteristics, nearest neighbour distance,… The natural question is: which morphological parameters provide the best statistical description of permeability? This question can be difficult to answer for several reasons: non-linear correlation between input parameters, non-linear correlation between inputs and outputs, small dataset, variability,…
A method of feature selection based on Gaussian Process Regression has been proposed. It can be applied to a wide range of applications where the parameters that best explain a given output are sought among a set of correlated features. The method uses anisotropic kernel that associates a hyperparameter to each feature. These hyperparameters can be interpreted as correlation lengths providing an estimation of the weight of each feature w.r.t the output.