Uncertainty Quantification

Lecturer Dr. E. Zander


Assistant


Schedule

Lectures: Thu 13:15-14:45 o'clock in room 812, Mühlenpfordtstr. 23 (Seminarraum WiRe)

Exercises: Thu 15:00-16:30 o'clock in room 826, Mühlenpfordtstr. 23 (Computerpool WiRe)

NEW: Excercise on the 18.05.2017 was moved to the 24.05.2017, Wednesday, 16:30-18:00 o'clock in room 826, Mühlenpfordtstr. 23 (Computerpool WiRe) - see below the homework

Thursday, 06.04.2017

• Lecture 1: Introduction, basics of probability theory
• Lecture 2: Basics of probability theory
• Lecture 3:Lebesgue integration, moments, MC integration, weak low of large numbers
• Lecture 4: Different type of equivalencies of RVs, and convergences, Latin Hypercubic Sampling and the QMC and their convergence
• Lecture 5: QMC, direct integration : Gauß quadrature
• Lecture 6: Orthogonal polynomials, direct integration in multiple dimension - the full tensor grid and the sparse grid integration rules
• Lecture 7: Spectral methods - preliminaries (separability, function approximationdenseness), multivariate gPCEs, multiindices, statistics from gPCE
• Lecture 8: Sparse integration rules, response surface methods: orthogonal projection
• Lecture 9: Response surface methods: projection theory, interpolation, regression, stochastic Galerkin method
• Lecture 10-11: Low-rank representation of random fields (processes) - KLE, Fourier...
• Lecture 12: Parameter estimation - introduction, the Bayes theorem, Markov Chains, Markov property
• Lecture 13: Parameter estimation (MCMC)
• Lecture 14: Parameter estimation (MMSE)

There is no script yet, but an ongoing effort to create one alongside with the lecture. You can see it here, but be aware that it's far from finished. If you spot any errors or inaccuracies or you have any suggestions, please send them to the lecturer of this course.

You can download the software for this course by issuing the following command on the command line:

git clone git://github.com/ezander/sglib-testing

This will create a directory sglib-testing for you, which will contain all the necessary files. Please start matlab from this directory, so that sglib can do its initialisation.

Tutorial 0 - Introduction to SGLIB and Probability Theory

Tutorial 1 - PDFs, CDFs, sampling from different distributions, transformation of Random Variables

• Example1 (Approximation of CDF and PDF from sampling)
• Example2 (CDFs, PDFs, moments and sampling with the GENDIST functions)
• Example3 (Transformation of Random Variables)

Tutorial 2,3 - Monte Carlo and Quasi Monte Carlo Integrations

• Example1 (Sampling with SimParameter and SimParamset)
• Example2 (Convergence of the Monte Carlo, and the Quasi Monte Carlo)

Tutorial 4,5 - Direct integration method, abstract framework of UQ and its implementation

• A toy example, oscillating mass: Plot true response surface (reference surface)
• Generating integration points I. (version in a more educative form)
• Generating integration points II. (version which is more practical)
• Compare sparse and full tensor grids
• Direct integration on a toy example
• Some small presentation of the idea of sparse grid

To be reviewed till the excercise on the 24.05.2017: Sampling from correlated random variables, the function sglib-testing\demo\lecture\norta\demo_norta2.m

Whether there will be a test or oral exams will be decided in the course of this semester.