Data-driven acceleration of multiscale methods for uncertainty quantification: application in transient multiphase flow in porous media

Multiscale methods aim to address the computational cost of elliptic problems on extremely large grids, by using numerically computed basis functions to reduce the dimensionality and complexity of the task. When multiscale methods are applied in uncertainty quantification to solve for a large number of parameter realizations, these basis functions need to be computed repeatedly for each realization. In our recent work (Chan et al. in J Comput Phys 354:493–511, 2017), we introduced a data-driven approach to further accelerate multiscale methods within uncertainty quantification. The basic idea is to construct a surrogate model to generate such basis functions at a much faster speed. The surrogate is modeled using a dataset of computed basis functions collected from a few runs of the multiscale method. Our previous study showed the effectiveness of this framework where speedups of two orders of magnitude were achieved in computing the basis functions while maintaining very good accuracy, however the study was limited to tracer flow/steady state flow problems. In this work, we extend the study to cover transient multiphase flow in porous media and provide further assessments.