An efficient stochastic approach for flow in porous media via sparse polynomial chaos expansion constructed by feature selection

Abstract

An efficient method for uncertainty quantification for flow in porous media is studied in this paper, where response surface of sparse polynomial chaos expansion (PCE) is constructed with the aid of feature selection method. The number of basis functions in PCE grows exponentially as the random dimensionality increases, which makes the computational cost unaffordable in high-dimensional problems. In this study, a feature selection method is introduced to select major stochastic features for the PCE by running a limited number of simulations, and the resultant PCE is termed as sparse PCE. Specifically, the least absolute shrinkage and selection operator modified least angle regression algorithm (LASSO-LAR) is applied for feature selection and the selected features are assessed by cross-validation (CV). Besides, inherited samples are utilized to make the algorithm self-adaptive. In this study, we test the performance of sparse PCE for uncertainty quantification for flow in heterogeneous media with different spatial variability. The statistical moments and probability density function of the output random field are accurately estimated through the sparse PCE, meanwhile the computational efforts are greatly reduced compared to the Monte Carlo method.