Stochastic representation and dimension reduction for non-Gaussian random fields: review and reflection

Abstract

This paper presents a review of methods for stochastic representation of non-Gaussian random fields. One category of such methods is through transformation from Gaussian random fields, and the other category is through direct simulation. This paper also gives a reflection on the simulation of non-Gaussian random fields, with the focus on its primary application for uncertainty quantification, which is usually associated with a large number of simulations. Dimension reduction is critical in the representation of non-Gaussian random fields with the aim of efficient uncertainty quantification. Aside from introducing the methods for simulating non-Gaussian random fields, critical components related to suitable stochastic approaches for efficient uncertainty quantification are stressed in this paper. Numerical examples of stochastic groundwater flow are also presented to investigate the applicability and efficiency of the methods for simulating non-Gaussian random fields for the purpose of uncertainty quantification.