Algorithms for Uncertainty Quantification - Summer 17
From Sccswiki
- Term
- Summer 17
- Lecturer
- Dr. Tobias Neckel
- Time and Place
- Lecture: Tuesday, 14:15-15:45 MI 02.07.023
- Tutorial: Wednesday, 12:15-13:45 MI 02.07.023
- Audience
- tba
- Tutorials
- Ionut Farcas
- Exam
- tba
- Semesterwochenstunden / ECTS Credits
- 4 SWS (2V+2Ü) / 5 Credits
- TUMonline
- Algorithms for UQ
Contents |
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 our 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
Announcements
- Exam: news below: there now is a separate section with details on the exam below.
- The lecture scheduled on June 6 2017 is cancelled
- The tutorial scheduled on June 7 2017 is cancelled
Lecture Slides
Lecture slides are published here successively.
- Introduction - April 25
- Repetition probability theory & statistics - May 02
- Intro sampling methods - May 09
- More advanced sampling methods - May 16
- Aspects of interpolation and quadrature - May 23
- Polynomial Chaos 1: the pseudo-spectral approach - May 30
- Polynomial Chaos 2: the stochastic Galerkin approach - June 13
- Sparse grids in Uncertainty Quantification - June 20
- Sensitivity analysis - June 28
- Random fields in Uncertainty Quantification - July 04
- Software for Uncertainty Quantification - July 11
- Guest lecture: Bayesian inverse problems - July 18
Worksheets and Solutions
Number | Topic | Worksheet | Tutorial | Solution |
---|---|---|---|---|
1 | Python overview | Worksheet1 | April 26 | Assignment 1, 2, 3 |
2 | Probability and statistics overview | Worksheet2 | May 03 | Assignment 1 Assignment 6 Solution worksheet2 |
3 | Standard Monte Carlo sampling | Worksheet3 | May 10 | Assignment 1 Assignment 2 Assignment 3 Assignment 4 |
4 | More advanced sampling techniques | Worksheet4 | May 17 | Assignment 1 Assignment 2.1 Assignment 2.2 |
5 | Aspects of interpolation and quadrature | Worksheet5 | May 24 | Assignment 1 Assignment 2 Assignment 3 |
6 | Polynomial Chaos 1: the pseudo-spectral approach | Worksheet6 | May 31 | Assignment 1 Assignment 2 |
7 | Polynomial Chaos 2: the stochastic Galerkin approach | Worksheet7 | June 14 | Solution worksheet7 |
8 | The sparse pseudo-spectral approach | Worksheet8 | June 21 | Assignment 1 Assignment 2 |
9 | Sobol' indices for global sensitivity analysis | Worksheet9 | June 28 | Assignment 2.1 Assignment 2.2 |
10 | Random fields in Uncertainty Quantification | Worksheet10 | July 05 | Assignment 1 Assignment 2 |
11 | Software for Uncertainty Quantification | Worksheet11 | July 12 | Solution worksheet11 |
Exam
- 2nd exam (check TUMonline):
- FRI, Oct 12, 10:30-11:45
- room: MI lecture hall 2
- review session: THU, Oct 19, 15:00, room 02.05.053
- first exam (check TUMonline):
- WED, Aug 02, 2017, 16:30-17:45 (75 min)
- room: MI lecture hall 2
- review session: WED, Aug 30, 2017, 12:30 - 13:15, seminar room 02.07.023
- covered topics: everything except:
- inverse problems (lecture 12)
- python programming
- specific API of chaospy (or other packages)
- style of exam exercises: similar to tutorials
- allowed material: one hand-written sheet of paper (size A4, possibly written on both pages). Only originals, no copies of such papers. No other material will be allowed!
- In case of a low number of registered candidates, the exam will be carried out orally (about 30 min).
Literature
- 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