Algorithms for Uncertainty Quantification - Summer 17
- Term
- Summer 17
- Lecturer
- Time and Place
- Lecture: tba
- Tutorial: tba
- Audience
- tba
- Tutorials
- tba
- Exam
- tba
- Semesterwochenstunden / ECTS Credits
- 4 SWS (2V+2Ü) / 5 Credits
- TUMonline
- tba
Contents
Computer simulations of different phenomena heavily rely on input data which – in many cases – are not known as exact values but face random effects. Uncertainty Quantification (UQ) is a cutting-edge research field that supports decision making under such uncertainties. Typical questions tackled in this course are “How to incorporate measurement errors into simulations and get a meaningful output?”, “What can I do to be 98.5% sure that my robot trajectory will be safe?”, “Which algorithms are available?”, “What is a good measure of complexity of UQ algorithms?”, “What is the potential for parallelization and High-Performance Computing of the different algorithms?”, or “Is there software available for UQ or do I need to program everything from scratch?” In particular, this course will cover
- Brief repetition of basic probability theory and statistics
- 1st class of algorithms: sampling methods for UQ (Monte Carlo): the brute-force approach
- More advanced sampling methods: Quasi Monte Carlo & Co.
- Relevant properties of interpolation & quadrature
- 2nd class of algorithms: stochastic collocation via the pseudo-spectral approach: Is it possible to obtain accurate results with (much) less costs?
- 3rd class of algorithms: stochastic Galerkin: Are we willing to (heavily) modify your software to gain accuracy?
- Dimensionality reduction in UQ: apply hierarchical methodologies such as tree-based sparse grid quadrature. How does the connection to Machine Learning and classification problems look like?
- Which parameters actually do matter? => sensitivity analysis (Sobol’ indices etc.)
- What if there is an infinite amount of parameters? => approximation methods for random fields (KL expansion)
- Software for UQ: What packages are available? What are the advantages and downsides of major players (such as chaospy, UQTk, and DAKOTA)
- Outlook: inverse UQ problems, data aspects, real-world measurements
Literatur
- R. C. Smith, Uncertainty Quantification – Theory, Implementation, and Applications, SIAM, 2014
- D. Xiu, Numerical Methods for Stochastic Computations – A Spectral Method Approach, Princeton Univ. Press, 2010
- T. J. Sullivan, Introduction to Uncertainty Quantification, Texts in Applied Mathematics 63, Springer, 2015