Bayesian Inference for Linear Parabolic PDEs with Noisy Boundary Conditions

Handle URI:
http://hdl.handle.net/10754/624068
Title:
Bayesian Inference for Linear Parabolic PDEs with Noisy Boundary Conditions
Authors:
Ruggeri, Fabrizio; Sawlan, Zaid A ( 0000-0002-4361-2491 ) ; Scavino, Marco ( 0000-0001-5114-853X ) ; Tempone, Raul ( 0000-0003-1967-4446 )
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.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences & Engineering (CEMSE)
Conference/Event name:
Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2015)
Issue Date:
7-Jan-2015
Type:
Poster
Appears in Collections:
Posters; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Conference on Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2015)

Full metadata record

DC FieldValue Language
dc.contributor.authorRuggeri, Fabrizioen
dc.contributor.authorSawlan, Zaid Aen
dc.contributor.authorScavino, Marcoen
dc.contributor.authorTempone, Raulen
dc.date.accessioned2017-06-05T08:35:47Z-
dc.date.available2017-06-05T08:35:47Z-
dc.date.issued2015-01-07-
dc.identifier.urihttp://hdl.handle.net/10754/624068-
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.en
dc.titleBayesian Inference for Linear Parabolic PDEs with Noisy Boundary Conditionsen
dc.typePosteren
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences & Engineering (CEMSE)en
dc.conference.dateJanuary 6-9, 2015en
dc.conference.nameAdvances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2015)en
dc.conference.locationKAUSTen
dc.contributor.institutionConsiglio Nazionale delle Ricercheen
dc.contributor.institutionUniversidad de la Rep├║blicaen
kaust.authorSawlan, Zaid Aen
kaust.authorScavino, Marcoen
kaust.authorTempone, Raulen
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