19223901
Lecture
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.
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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.
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