Nonparametric Belief Propagation Method for Uncertainty Quantification with Applications to Flow in Random Porous Media.

摘要

We develop a nonparametric belief propagation method for uncertainty quantification and apply it to model flow in random porous media. The relationship between the high-dimensional input and the multi-output responses is addressed by breaking the global regression problem into smaller local problems using probabilistic links. These links can be well represented in a probabilistic graphical model. The whole framework is designed to be nonparametric (Gaussian mixture) in order to capture the non-Gaussian features of the response. With the known input distribution, a loopy nonparametric belief propagation algorithm is used to find the corresponding marginal distributions of the responses. The probabilistic graphical framework can be used as a surrogate model to predict the responses for new input realizations as well as our confidence on these predictions. Numerical examples are presented to show the accuracy and efficiency of the probabilistic graphical model framework and nonparametric belief propagation method for solving uncertainty quantification problems in flows in porous media using stationary and non-stationary permeability fields.