MPI Kolloquiumsreihe: Prof. Dr. Albert Cohen: Reduced Model Estimation from Data Measurements
MPI Kolloquiumsreihe: Prof. Dr. Albert Cohen, Université Pierre et Marie Curie, Paris
- Datum: 31.05.2018
- Uhrzeit: 16:00 - 18:00
- Vortragende(r): Prof. Dr. Albert Cohen, Université Pierre et Marie Curie, Paris
- Laboratoire Jacques-Louis Lions
- Ort: Lukasklause (Otto-von-Guericke-Zentrum), Schleinufer 1, 39104 Magdeburg
- 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
Das Max-Planck-Institut Magdeburg und die Fakultät für Mathematik der OVGU laden Sie herzlich zur öffentlichen Kolloquiumsreihe ein.
Hochrangige Wissenschaftler aus verschiedenen Fachgebieten, eingeladen vom Max-Planck-Institut Magdeburg, präsentieren ihre Forschungsarbeit.
Im Anschluss an das Kolloquium lädt die Otto-von-Guericke-Universität Magdeburg zur Antrittsvorlesung von Frau Prof. Dr. Alexandra Carpentier ein.
Reduced Model Estimation from Data Measurements
Abstract
One typical scenario in data assimilation is the following: one
observes m linear measurements of a function u which is solution to a
partial differential equation where certain parameters are unknown. The
measurement functionals are picked
from a certain dictionary D, for
example when placing sensors at m chosen locations. The state
estimation problem then consists in recovering u from these
measurements.
One possible approach to this problem exploits the
fact that the family of solution for all potential parameter values is
well approximated by linear spaces of moderate dimension n. Such spaces
are typically obtained by reduced model techniques, such as reduced
bases, proper orthogonal polynomial expansions in the parametric
variable.
The numerical method achieves a reconstruction which
has the accuracy of the best approximation from the n-dimensional space
to the unknown solution u, up to a multiplicative constant which takes
the form of an inverse inf-sup constant between the approximation space
and the spacegenerated by the Riesz representers of the linear forms
giving rise to the measurements.
One issue discussed in this talk
is how to select the measurement functionals within D to maintain this
constant of reasonable size, with m as small as possible. In
particular, we present a greedy algorithm allowing for a stepwise
selection process of reasonable computational cost, and we analyze its
properties.