A modified differential evolution McMC with fewer chains: A study on a porous media application

Resumo

Quantifying uncertainties in porous media flow problems usually involves high-dimensional stochastic spaces that make the application of Markov chain Monte Carlo methods computationally inefficient. Several measures can be taken to reduce this problem, including dimensionality reduction via Karhunen-Loève expansion or generative neural networks, in addition to adjusting the jump and direction of the proposals. However, this reduced problems still suffer from convergence, demanding sampling methods that cover the parametric space more effectively. Some of them imply higher computational cost. In this context, we propose modifications of the Differential evolution-based Markov chain Monte Carlo (DE-McMC) method, aiming to accelerate the convergence of the chains without a prohibitive increase in the number of chains that depend on the stochastic dimension. Outlier detection is also included to speed up the convergence. The gain in performance is shown through a benchmark comparative study performed on a 2D five-spot problem application.