Inverse problems and uncertainty quantification

Handle URI:
http://hdl.handle.net/10754/623698
Title:
Inverse problems and uncertainty quantification
Authors:
Litvinenko, Alexander ( 0000-0001-5427-3598 ) ; Matthies, Hermann G.
Abstract:
In a Bayesian setting, inverse problems and uncertainty quantification (UQ)— the propagation of uncertainty through a computational (forward) model—are 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.
KAUST Department:
SRI Uncertainty Quantification Center; Extreme Computing Research Center
Issue Date:
18-Dec-2013
ARXIV:
arXiv:1312.5048
Type:
Technical Report
Series/Report no.:
Subjects: Numerical Analysis (math.NA) MSC classes: 62F15, 65N21, 62P30, 60H15, 60H25, 74G75, 80A23, 74C05
Sponsors:
KAUST, DFG
Additional Links:
https://arxiv.org/abs/1312.5048
Appears in Collections:
Technical Reports

Full metadata record

DC FieldValue Language
dc.contributor.authorLitvinenko, Alexanderen
dc.contributor.authorMatthies, Hermann G.en
dc.date.accessioned2017-05-23T07:50:14Z-
dc.date.available2017-05-23T07:50:14Z-
dc.date.issued2013-12-18-
dc.identifier.urihttp://hdl.handle.net/10754/623698-
dc.description.abstractIn a Bayesian setting, inverse problems and uncertainty quantification (UQ)— the propagation of uncertainty through a computational (forward) model—are 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.en
dc.description.sponsorshipKAUST, DFGen
dc.relation.ispartofseriesSubjects: Numerical Analysis (math.NA) MSC classes: 62F15, 65N21, 62P30, 60H15, 60H25, 74G75, 80A23, 74C05en
dc.relation.urlhttps://arxiv.org/abs/1312.5048en
dc.subjectinverse problemsen
dc.subjectBayesian update surrogateen
dc.subjectBayesian update PCEen
dc.subjectPolynomial chaos expansionen
dc.subjectsampling free non-linearen
dc.subjectLorenz 84en
dc.subjectconditional expectationen
dc.subjectMMSEen
dc.titleInverse problems and uncertainty quantificationen
dc.typeTechnical Reporten
dc.contributor.departmentSRI Uncertainty Quantification Centeren
dc.contributor.departmentExtreme Computing Research Centeren
dc.contributor.institutionTechnische Universitaet Braunschweigen
dc.identifier.arxividarXiv:1312.5048en
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