19223901
Lecture
WiSe 22/23: Uncertainty Quantification and quasi-Monte Carlo
Claudia Schillings
Comments
High-dimensional numerical integration plays a central role in contemporary study of uncertainty quantification. The analysis of how uncertainties associated with material parameters or the measurement configuration propagate within mathematical models leads to challenging high-dimensional integration problems, fueling the need to develop efficient numerical methods for this task.
Modern quasi-Monte Carlo (QMC) methods are based on tailoring specially designed cubature rules for high-dimensional integration problems. By leveraging the smoothness and anisotropy of an integrand, it is possible to achieve faster-than-Monte Carlo convergence rates. QMC methods have become a popular tool for solving partial differential equations (PDEs) involving random coefficients, a central topic within the field of uncertainty quantification.
This course provides an introduction to uncertainty quantification and how QMC methods can be applied to solve problems arising within this field.
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.
16 Class schedule
Regular appointments
Mon, 2022-10-17 12:00 - 14:00
Uncertainty Quantification and quasi-Monte Carlo
Mon, 2022-10-24 12:00 - 14:00
Uncertainty Quantification and quasi-Monte Carlo
Mon, 2022-10-31 12:00 - 14:00
Uncertainty Quantification and quasi-Monte Carlo
Mon, 2022-11-07 12:00 - 14:00
Uncertainty Quantification and quasi-Monte Carlo
Mon, 2022-11-14 12:00 - 14:00
Uncertainty Quantification and quasi-Monte Carlo
Mon, 2022-11-21 12:00 - 14:00
Uncertainty Quantification and quasi-Monte Carlo
Mon, 2022-11-28 12:00 - 14:00
Uncertainty Quantification and quasi-Monte Carlo
Mon, 2022-12-05 12:00 - 14:00
Uncertainty Quantification and quasi-Monte Carlo
Mon, 2022-12-12 12:00 - 14:00
Uncertainty Quantification and quasi-Monte Carlo
Mon, 2023-01-02 12:00 - 14:00
Uncertainty Quantification and quasi-Monte Carlo
Mon, 2023-01-09 12:00 - 14:00
Uncertainty Quantification and quasi-Monte Carlo
Mon, 2023-01-16 12:00 - 14:00
Uncertainty Quantification and quasi-Monte Carlo
Mon, 2023-01-23 12:00 - 14:00
Uncertainty Quantification and quasi-Monte Carlo
Mon, 2023-01-30 12:00 - 14:00
Uncertainty Quantification and quasi-Monte Carlo
Mon, 2023-02-06 12:00 - 14:00
Uncertainty Quantification and quasi-Monte Carlo
Mon, 2023-02-13 12:00 - 14:00
Uncertainty Quantification and quasi-Monte Carlo