19223901
Lecture
SoSe 24: Uncertainty Quantification & Inverse Problems
Claudia Schillings
Comments
Uncertainty Quantification and Inverse Problems
Inverse problems and uncertainty quantification are closely related fields essential in many scientific and engineering disciplines. Inverse problems involve deducing unknown causes or system parameters from observed effects (data), often encountered in areas like medical imaging or geophysics. These problems are challenging due to issues like non-uniqueness and instability. Uncertainty quantification complements this by assessing and managing the uncertainty in models and simulations, crucial for making reliable predictions. Together, these disciplines focus on developing robust methods for understanding and predicting complex systems despite inherent uncertainties and limited data.
In this course, we will cover the following topics:
- basics from probability theory and functional analysis
- inverse problems and optimization
- Bayesian (regularization of) inverse problems
- measures of information and uncertainty; Bayesian experimental design
- Gaussian process regression
- sampling (Monte Carlo, importance sampling, MCMC) for numerical integration in high dimensions
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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.
13 Class schedule
Regular appointments
Mon, 2024-04-15 10:00 - 12:00
Uncertainty Quantification & Inverse Problems
Mon, 2024-04-22 10:00 - 12:00
Uncertainty Quantification & Inverse Problems
Mon, 2024-04-29 10:00 - 12:00
Uncertainty Quantification & Inverse Problems
Mon, 2024-05-06 10:00 - 12:00
Uncertainty Quantification & Inverse Problems
Mon, 2024-05-13 10:00 - 12:00
Uncertainty Quantification & Inverse Problems
Mon, 2024-05-27 10:00 - 12:00
Uncertainty Quantification & Inverse Problems
Mon, 2024-06-03 10:00 - 12:00
Uncertainty Quantification & Inverse Problems
Mon, 2024-06-10 10:00 - 12:00
Uncertainty Quantification & Inverse Problems
Mon, 2024-06-17 10:00 - 12:00
Uncertainty Quantification & Inverse Problems
Mon, 2024-06-24 10:00 - 12:00
Uncertainty Quantification & Inverse Problems
Mon, 2024-07-01 10:00 - 12:00
Uncertainty Quantification & Inverse Problems
Mon, 2024-07-08 10:00 - 12:00
Uncertainty Quantification & Inverse Problems
Mon, 2024-07-15 10:00 - 12:00
Uncertainty Quantification & Inverse Problems
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