Comparisons of FV-MHMM with other finite volume multiscale methods.

pscaling and multiscale methods in reservoir engineering remain a complicated task especially when dealing with heterogeneities. In this study, we focus on flow field problem with a Darcy’s equation considered at the fine scale. The main difficulty is then to obtain an accurate description of the flow behavior by using multiscale methods available in petroleum engineering. We cross-compare three of the main finite volume formulations: multiscale finite volume method (MsFv), multiscale restriction smoothed (MsRSB) and a new finite volume method, FV-MHMM. Comparisons are done in terms of accuracy to reproduce the fine scale behavior

A machine learning approach for efficient uncertainty quantification using multiscale methods

Several multiscale methods account for sub-grid scale features using coarse scale basis functions. For example, in the Multiscale Finite Volume method the coarse scale basis functions are obtained by solving a set of local problems over dual-grid cells. We introduce a data-driven approach for the estimation of these coarse scale basis functions. Specifically, we employ a neural network predictor fitted using a set of solution samples from which it learns to generate subsequent basis functions at a lower computational cost than solving the local problems. The computational advantage of this approach is realized for uncertainty quantification tasks where a large number of realizations has to be evaluated. We attribute the ability to learn these basis functions to the modularity of the local problems and the redundancy of the permeability patches between samples. The proposed method is evaluated on elliptic problems yielding very promising results.Comment: Journal of Computational Physics (2017