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    Inverse Problems and Uncertainty Quantification

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    Type
    Presentation
    Authors
    Litvinenko, Alexander cc
    Matthies, Hermann G.
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Date
    2014-01-06
    Permanent link to this record
    http://hdl.handle.net/10754/624019
    
    Metadata
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    Abstract
    In a Bayesian setting, inverse problems and uncertainty quantification (UQ) - the propagation of uncertainty through a computational (forward) modelare strongly connected. In the form of conditional expectation the Bayesian update becomes computationally attractive. This is especially the case as together with a functional or spectral approach for the forward UQ there is no need for time- consuming and slowly convergent Monte Carlo sampling. The developed sampling- free non-linear Bayesian update is derived from the variational problem associated with conditional expectation. This formulation in general calls for further discretisa- tion to make the computation possible, and we choose a polynomial approximation. After giving details on the actual computation in the framework of functional or spectral approximations, we demonstrate the workings of the algorithm on a number of examples of increasing complexity. At last, we compare the linear and quadratic Bayesian update on the small but taxing example of the chaotic Lorenz 84 model, where we experiment with the influence of different observation or measurement operators on the update.
    Conference/Event name
    Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2014)
    Additional Links
    http://mediasite.kaust.edu.sa/Mediasite/Play/c9df2ecfa32949fd8dd0dbc4d82099801d?catalog=ca65101c-a4eb-4057-9444-45f799bd9c52
    Collections
    Presentations; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division; Conference on Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2014)

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