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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Veröffentlicht in:Journal of computational physics Jg. 272; S. 664 - 685
Hauptverfasser: Wan, Jiang, Zabaras, Nicholas
Format: Journal Article
Sprache:Englisch
Veröffentlicht: United States Elsevier Inc 01.09.2014
Schlagworte:
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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Zusammenfassung: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.
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ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2014.05.002