MPI Kolloquiumsreihe: Univ.-Prof. Dipl.-Ing. Dr. Barbara Kaltenbacher: Iterative regularization of time-dependent inverse problems
MPI Kolloquiumsreihe: Univ.-Prof. Dipl.-Ing. Dr. Barbara Kaltenbacher: Iterative regularization of time-dependent inverse problems
- Datum: 10.01.2019
- Uhrzeit: 17:00 - 18:00
- Vortragende(r): Univ.-Prof. Dipl.-Ing. Dr. Barbara Kaltenbacher
- Institut für Mathematik, Universität Klagenfurt, Österreich
- Ort: Max-Planck-Institut Magdeburg
- Raum: Großer Seminarraum "Prigogine"
- Gastgeber: veranstaltet vom Max-Planck-Institut Magdeburg und der Fakultät für Mathematik an der Otto-von-Guericke-Universität Magdeburg
- Kontakt: sek-csc@mpi-magdeburg.mpg.de
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Iterative regularization of time-dependent inverse problems
Abstract:
A large number of inverse problems in applications ranging from
engineering via economics to systems biology can be formulated as a
nonlinear state space system, where some finite or infinite dimensional
parameter is supposed to be identified from additional continuous or
discrete indirect observations. This will be illustrated by some
parameter identification problems in time dependent partial differential
equations.
Due to the ill-posedness of such
inverse problems -- especially in case of infinite dimensional
parameters -- the problem needs to be regularized.
The focus
of this talk will be on the use of iterative (gradient or Newton type)
methods for this purpose, where regularization is achieved by early
stopping. We will highlight the difference between classical reduced
formulations based on a parameter-to-state-map, and an all-at-once
approach. Moreover, we will consider a splitting of these inverse
problems into smaller subsystems, by means of a subdivision of the time
line in subintervals, as well as cyclic iterations over these
subproblems -- so-called Kaczmarz methods.