A probabilistic graphical model based stochastic input model construction

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 dimens...

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Vydané v:	Journal of computational physics Ročník 272; s. 664 - 685
Hlavní autori:	Wan, Jiang, Zabaras, Nicholas
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	United States Elsevier Inc 01.09.2014
Predmet:	ACCURACY ALGORITHMS CHAOS THEORY CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS Computation COMPUTERIZED SIMULATION Constraint-based algorithm Karhunen–Loève (KL) expansion Kernel PCA KERNELS LIMITING VALUES MATHEMATICAL MODELS MATHEMATICAL SOLUTIONS Model reduction NONLINEAR PROBLEMS Polynomial chaos expansion POLYNOMIALS Portable document format PROBABILISTIC ESTIMATION Probabilistic graphical model structure learning Probabilistic methods Probability theory Random variables RANDOMNESS STOCHASTIC PROCESSES Stochasticity Constraint-based algorithm Kernel PCA Probabilistic graphical model structure learning Polynomial chaos expansion Karhunen–Loève (KL) expansion
ISSN:	0021-9991, 1090-2716
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Popis
Shrnutí:	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. •Data-driven stochastic input models without the assumption of independence of the reduced random variables.•The problem is transformed to a Bayesian network structure learning problem.•Examples are given in flows in random media.
Bibliografia:	ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23 ObjectType-Article-1 ObjectType-Feature-2
ISSN:	0021-9991 1090-2716
DOI:	10.1016/j.jcp.2014.05.002