Show simple item record

dc.contributor.author
Lanthaler, Samuel
dc.contributor.author
Mishra, Siddhartha
dc.contributor.author
Weber, Franziska
dc.date.accessioned
2021-07-30T07:10:23Z
dc.date.available
2021-07-27T08:03:35Z
dc.date.available
2021-07-30T07:10:23Z
dc.date.issued
2021-07
dc.identifier.uri
http://hdl.handle.net/20.500.11850/497830
dc.description.abstract
We study the well-posedness of Bayesian inverse problems for PDEs, for which the underlying forward problem may be ill-posed. Such PDEs, which include the fundamental equations of fluid dynamics, are characterized by the lack of rigorous global existence and stability results as well as possible non-convergence of numerical approximations. Under very general hypotheses on approximations to these PDEs, we prove that the posterior measure, expressing the solution of the Bayesian inverse problem, exists and is stable with respect to perturbations of the (noisy) measurements. Moreover, analogous well-posedness results are obtained for the data assimilation (filtering) problem in the time-dependent setting. Finally, we apply this abstract framework to the incompressible Euler and Navier-Stokes equations and to hyperbolic systems of conservation laws and demonstrate well-posedness results for the Bayesian inverse and filtering problems, even when the underlying forward problem may be ill-posed.
en_US
dc.language.iso
en
en_US
dc.publisher
Seminar for Applied Mathematics, ETH Zurich
en_US
dc.title
On the well-posedness of Bayesian inversion for PDEs with ill-posed forward problems
en_US
dc.type
Report
ethz.journal.title
SAM Research Report
ethz.journal.volume
2021-22
en_US
ethz.size
44 p.
en_US
ethz.publication.place
Zurich
en_US
ethz.publication.status
published
en_US
ethz.leitzahl
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02501 - Seminar für Angewandte Mathematik / Seminar for Applied Mathematics::03851 - Mishra, Siddhartha / Mishra, Siddhartha
en_US
ethz.leitzahl.certified
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02501 - Seminar für Angewandte Mathematik / Seminar for Applied Mathematics::03851 - Mishra, Siddhartha / Mishra, Siddhartha
en_US
ethz.identifier.url
https://math.ethz.ch/sam/research/reports.html?id=964
ethz.date.deposited
2021-07-27T08:03:41Z
ethz.source
FORM
ethz.eth
yes
en_US
ethz.identifier.internal
https://math.ethz.ch/sam/research/reports.html?id=964
en_US
ethz.availability
Metadata only
en_US
ethz.rosetta.installDate
2021-07-30T07:10:29Z
ethz.rosetta.lastUpdated
2021-07-30T07:10:29Z
ethz.rosetta.versionExported
true
ethz.COinS
ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.atitle=On%20the%20well-posedness%20of%20Bayesian%20inversion%20for%20PDEs%20with%20ill-posed%20forward%20problems&rft.jtitle=SAM%20Research%20Report&rft.date=2021-07&rft.volume=2021-22&rft.au=Lanthaler,%20Samuel&Mishra,%20Siddhartha&Weber,%20Franziska&rft.genre=report&
 Search print copy at ETH Library

Files in this item

FilesSizeFormatOpen in viewer

There are no files associated with this item.

Publication type

Show simple item record