A prefetching technique for prediction of porous media flows

In many applications in flows through porous media, one needs to determine the properties of subsurface to detect, monitor, or predict the actions of natural or induced forces. Here, we focus on two important subsurface properties: rock permeability and porosity. A Bayesian approach using a Markov Chain Monte Carlo (MCMC) algorithm is well suited for reconstructing the spatial distribution of permeability and porosity, and quantifying associated uncertainty in these properties. A crucial step in this approach is the computation of a likelihood function, which involves solving a possibly nonlinear system of partial differential equations. The computation time for the likelihood function limits the number of MCMC iterations that can be performed in a practical period of time. This affects the consistency of the posterior distribution of permeability and porosity obtained by MCMC exploration. To speed-up the posterior exploration, we can use a prefetching technique, which relies on the fact that multiple likelihoods of possible states into the future in an MCMC chain can be computed ahead of time. In this paper, we show that the prefetching technique implemented on multiple processors can make the Bayesian approach computationally tractable for subsurface characterization and prediction of porous media flows.