Algorithms for Uncertainty Quantification - Summer 18

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Term
Summer 18
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
Master students, e.g. of CSE, mathematics, informatics, data science, data engineering and analytics, physics,...
Tutorials
Friedrich Menhorn
Exam
preliminary: 01.08.2018, 11:00-12:15
Semesterwochenstunden / ECTS Credits
4 SWS (2V+2Ü) / 5 Credits
TUMonline
Algorithms for UQ (IN2345)



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

  • The first lecture takes place on April 10 2018.

Lecture Slides

determ. simulator, ODE solver, config file, MC simulator, approximation of pi

Worksheets and Solutions

Number Topic Worksheet Tutorial Code Solution
1 Python overview Worksheet1 April 11 Template Solution 1 Solution 2 Solution 3
2 Probability and statistics overview Worksheet2 May 02 Solution 1 Solution 6 Solution.pdf
3 Standard Monte Carlo sampling Worksheet3 May 9 Template

Exam

  • first exam (preliminary, check TUMonline):
    • WED, Aug 01, 2018, 11:00-12:15 (75 min)
  • covered topics (preliminary): everything except:
    • inverse problems (lecture 12)
    • python programming
    • specific API of chaospy (or other packages)
  • style of exam exercises: similar to tutorials
  • allowed material: tba
  • Most likely written exam. However, 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
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