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dc.contributor.authorRuggeri, Fabrizio
dc.contributor.authorSawlan, Zaid A
dc.contributor.authorScavino, Marco
dc.contributor.authorTempone, Raul
dc.date.accessioned2017-06-08T06:32:26Z
dc.date.available2017-06-08T06:32:26Z
dc.date.issued2016-01-06
dc.identifier.urihttp://hdl.handle.net/10754/624796
dc.description.abstractIn 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.
dc.subjectBayesian
dc.titleBayesian Inference for Linear Parabolic PDEs with Noisy Boundary Conditions
dc.typePoster
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.conference.dateJanuary 5-10, 2016
dc.conference.nameAdvances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2016)
dc.conference.locationKAUST
dc.contributor.institutionIstituto di Matematica Applicata e Tecnologie Informatiche
kaust.personSawlan, Zaid A
kaust.personScavino, Marco
kaust.personTempone, Raul
refterms.dateFOA2018-06-13T11:44:42Z


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