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    Bayesian Inference for Linear Parabolic PDEs with Noisy Boundary Conditions

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    Type
    Poster
    Authors
    Ruggeri, Fabrizio
    Sawlan, Zaid A cc
    Scavino, Marco cc
    Tempone, Raul cc
    KAUST Department
    Applied Mathematics and Computational Science Program
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Date
    2015-01-07
    Permanent link to this record
    http://hdl.handle.net/10754/624068
    
    Metadata
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    Abstract
    In this work we develop a hierarchical Bayesian setting to infer unknown parameters in initial-boundary value problems (IBVPs) for one-dimensional linear parabolic partial differential equations. Noisy boundary data and known initial condition are assumed. We derive the likelihood function associated with the forward problem, given some measurements of the solution field subject to Gaussian noise. Such function is then analytically marginalized using the linearity of the equation. Gaussian priors have been assumed for the time-dependent Dirichlet boundary values. Our approach is applied to synthetic data for the one-dimensional heat equation model, where the thermal diffusivity is the unknown parameter. We show how to infer the thermal diffusivity parameter when its prior distribution is lognormal or modeled by means of a space-dependent stationary lognormal random field. We use the Laplace method to provide approximated Gaussian posterior distributions for the thermal diffusivity. Expected information gains and predictive posterior densities for observable quantities are numerically estimated for different experimental setups.
    Conference/Event name
    Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2015)
    Collections
    Posters; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division; Conference on Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2015)

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