Algorithms for Uncertainty Quantification - Summer 17

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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

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.


Worksheets and Solutions

Number Topic Worksheet Tutorial Solution
1 Python overview Worksheet1 April 26
2 Probability and statistics overview Worksheet2 May 03
3 Standard Monte Carlo sampling Worksheet3 May 10
4 More advanced sampling techniques Worksheet4 May 17
5 Aspects of interpolation and quadrature Worksheet5 May 24
6 Polynomial Chaos 1: the pseudo-spectral approach Worksheet6 May 31
7 Polynomial Chaos 2: the stochastic Galerkin approach Worksheet7 June 14
8 The sparse pseudo-spectral approach Worksheet8 June 21
9 Sobol' indices for global sensitivity analysis Worksheet9 June 28
10 Random fields in Uncertainty Quantification Worksheet10 July 05
11 Software for Uncertainty Quantification Worksheet11 July 12

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
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