19223901
Lecture
SoSe 22: Inverse Problems
Vesa Kaarnioja, Claudia Schillings
Comments
Mathematical measurement models describe the causal effects of physical systems based on their material properties, initial conditions or other model parameters. In many practical problems, we have measurement data of the outcomes of these so-called "forward models" and we wish to infer the model parameters which caused the observations. This is an inverse problem.
Inverse problems are intrinsically ill-posed: the reconstruction of the unknown quantity may be highly sensitive to noise in the measurements, or a unique solution may not exist. For these reasons, regularization is an essential tool in order to find solutions to inverse problems. In this course, we will consider both deterministic regularization methods and statistical Bayesian inference. We will discuss the main challenges related to inverse problems as well as the main solution techniques. close
Suggested reading
The following books will be relevant:
- O. P. Le Maître and O. M. Knio. Spectral Methods for Uncertainty Quantification: With Applications to Computational Fluid Dynamics. Scientific Computation. Springer, New York, 2010.
- R. C. Smith. Uncertainty Quantification: Theory, Implementation, and Applications, volume 12 of Computational Science & Engineering. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2014.
- T. J. Sullivan. Introduction to Uncertainty Quantification. Springer, New York, in press.
- D. Xiu. Numerical Methods for Stochastic Computations: A Spectral Method Approach. Princeton University Press, Princeton, NJ, 2010.
25 Class schedule
Regular appointments
Mon, 2022-04-25 10:00 - 12:00
Inverse Problems
Mon, 2022-05-02 10:00 - 12:00
Inverse Problems
Mon, 2022-05-09 10:00 - 12:00
Inverse Problems
Mon, 2022-05-16 10:00 - 12:00
Inverse Problems
Mon, 2022-05-23 10:00 - 12:00
Inverse Problems
Mon, 2022-05-30 10:00 - 12:00
Inverse Problems
Mon, 2022-06-13 10:00 - 12:00
Inverse Problems
Mon, 2022-06-20 10:00 - 12:00
Inverse Problems
Mon, 2022-06-27 10:00 - 12:00
Inverse Problems
Mon, 2022-07-04 10:00 - 12:00
Inverse Problems
Mon, 2022-07-11 10:00 - 12:00
Inverse Problems
Mon, 2022-07-18 10:00 - 12:00
Inverse Problems
Mon, 2022-04-25 10:00 - 12:00
Mon, 2022-05-02 10:00 - 12:00
Mon, 2022-05-09 10:00 - 12:00
Mon, 2022-05-16 10:00 - 12:00
Mon, 2022-05-23 10:00 - 12:00
Mon, 2022-05-30 10:00 - 12:00
Mon, 2022-06-06 10:00 - 12:00
Mon, 2022-06-20 10:00 - 12:00
Mon, 2022-06-27 10:00 - 12:00
Mon, 2022-07-04 10:00 - 12:00
Mon, 2022-07-11 10:00 - 12:00
Mon, 2022-07-18 10:00 - 12:00
Inverse Problems
Inverse Problems
Inverse Problems
Inverse Problems
Inverse Problems
Inverse Problems
Inverse Problems
Mon, 2022-06-13 10:00 - 12:00
Inverse Problems
Inverse Problems
Inverse Problems
Inverse Problems
Inverse Problems
Inverse Problems