Article: Wan J, Zabaras N; (2014) A Probabilistic Graphical Model Based Stochastic Input Model Construction, Journal of Computational Physics, 272: 664-685
Abstract: Model reduction techniques have been widely used in modeling of high-dimensional stochastic input in uncertainty quantification tasks.
However, the probabilistic modeling of random variables projected into reduced-order spaces presents a number of computational challenges. Due to the curse of dimensionality, the underlying dependence relationships between these random variables are difficult to capture. In this work, a probabilistic graphical model based approach is employed to learn the dependence by running a number of conditional independence tests using observation data. Thus a probabilistic model of the joint PDF is obtained and the PDF is factorized into a set of conditional distributions based on the dependence structure of the variables. The estimation of the joint PDF from data is then transformed to estimating conditional distributions under reduced dimensions. To improve the computational efficiency, a polynomial chaos expansion is further applied to represent the random field in terms of a set of standard random variables. This technique is combined with both linear and nonlinear model reduction methods. Numerical examples are presented to demonstrate the accuracy and efficiency of the probabilistic graphical model based stochastic input models. (C) 2014 Elsevier Inc. All rights reserved.