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Uncertainty Quantification and Quasi-Monte Carlo

News

  • The exercise room has changed. All lectures and exercises will now take place in room A6/032.
  • We will continue discussing the functional analytic preliminaries on Tuesday April 22, 10:15-11:45, in room A3/120.

Dates

Lectures Mon 10:15-11:45 A6/032 Dr. Vesa Kaarnioja
Exercises Tue 10:15-11:45 A6/032 Dr. Vesa Kaarnioja

General Information

Description

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.

Target audience

The course is intended for mathematics students at the Master's level and above.

Prerequisites

Multivariable calculus, linear algebra, basic probability theory, and Python (or some other programming language).

Completing the course

To be eligible to sit for the final exam, a student must earn a minimum of cumulative 60% points from the exercises. The course evaluation is based on the final exam.

Registration

  • Please register to the course via Campus Management (CM), then you will be automatically registered in MyCampus/Whiteboard as well. Please note the deadlines indicated there. For further information and in case of any problems, please consult the Campus Management's Help for Students.
  • Non-FU students should register to the course in KVV (Whiteboard).

Lecture notes

Lecture notes will be published here before each week's lecture.

Exercise sheets

Exercises will be published here regularly.

Contact

Dr. Vesa Kaarnioja vesa.kaarnioja@fu-berlin.de Arnimallee 6, room 212
Consulting hours: By appointment