Difference between revisions of "Algorithms for Uncertainty Quantification - Summer 17"

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! '''Number''' !! '''Topic''' !! '''Worksheet''' !! '''Tutorial''' !! '''Solution'''  
 
! '''Number''' !! '''Topic''' !! '''Worksheet''' !! '''Tutorial''' !! '''Solution'''  
 
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| 1 || Python overview || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt1/worksheet1.pdf Worksheet1] || April 26 || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt1/ex.py Assignment 1, 2, 3]
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| 1 || Python overview || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt1/worksheet1.pdf Worksheet1] || April 26 ||<!--  [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt1/ex.py Assignment 1, 2, 3]-->
 
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| 2 || Probability and statistics overview || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt2/worksheet2.pdf Worksheet2] || May 03 || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt2/ex1.py Assignment 1] [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt2/ex6.py Assignment 6] [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt2/worksheet2_sol.pdf Solution worksheet2]
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| 2 || Probability and statistics overview || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt2/worksheet2.pdf Worksheet2] || May 03 || <!-- [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt2/ex1.py Assignment 1] [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt2/ex6.py Assignment 6] [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt2/worksheet2_sol.pdf Solution worksheet2]-->
 
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| 3 || Standard Monte Carlo sampling || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt3/worksheet3.pdf Worksheet3] || May 10 || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt3/ex1.py Assignment 1] [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt3/ex2.py Assignment 2] [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt3/ex3.py Assignment 3] [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt3/ex4.py Assignment 4]
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| 3 || Standard Monte Carlo sampling || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt3/worksheet3.pdf Worksheet3] || May 10 || <!-- [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt3/ex1.py Assignment 1] [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt3/ex2.py Assignment 2] [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt3/ex3.py Assignment 3] [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt3/ex4.py Assignment 4]-->
 
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| 4 || More advanced sampling techniques || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt4/worksheet4.pdf Worksheet4] || May 17 || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt4/ex1.py Assignment 1] [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt4/ex2.1.py Assignment 2.1] [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt4/ex2.2.py Assignment 2.2]
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| 4 || More advanced sampling techniques || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt4/worksheet4.pdf Worksheet4] || May 17 || <!-- [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt4/ex1.py Assignment 1] [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt4/ex2.1.py Assignment 2.1] [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt4/ex2.2.py Assignment 2.2]-->
 
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| 5 || Aspects of interpolation and quadrature || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt5/worksheet5.pdf Worksheet5] || May 24 || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt5/ex1.py Assignment 1] [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt5/ex2.py Assignment 2] [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt5/ex3.py Assignment 3]
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| 5 || Aspects of interpolation and quadrature || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt5/worksheet5.pdf Worksheet5] || May 24 || <!-- [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt5/ex1.py Assignment 1] [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt5/ex2.py Assignment 2] [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt5/ex3.py Assignment 3]-->
 
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| 6 || Polynomial Chaos 1: the pseudo-spectral approach || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt6/worksheet6.pdf Worksheet6] || May 31 || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt6/ex1.py Assignment 1] [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt6/ex2.py Assignment 2]  
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| 6 || Polynomial Chaos 1: the pseudo-spectral approach || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt6/worksheet6.pdf Worksheet6] || May 31 || <!-- [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt6/ex1.py Assignment 1] [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt6/ex2.py Assignment 2] -->
 
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| 7 || Polynomial Chaos 2: the stochastic Galerkin approach || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt7/worksheet7.pdf Worksheet7] || June 14 || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt7/worksheet7_sol.pdf Solution worksheet7]
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| 7 || Polynomial Chaos 2: the stochastic Galerkin approach || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt7/worksheet7.pdf Worksheet7] || June 14 || <!-- [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt7/worksheet7_sol.pdf Solution worksheet7]-->
 
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| 8 || The sparse pseudo-spectral approach || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt8/worksheet8.pdf Worksheet8] || June 21 || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt8/ex1.py Assignment 1] [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt8/ex2.py Assignment 2]
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| 8 || The sparse pseudo-spectral approach || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt8/worksheet8.pdf Worksheet8] || June 21 ||<!--  [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt8/ex1.py Assignment 1] [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt8/ex2.py Assignment 2]-->
 
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| 9 || Sobol' indices for global sensitivity analysis || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt9/worksheet9.pdf Worksheet9] || June 28 || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt9/ex1.1.py Assignment 2.1] [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt9/ex1.2.py Assignment 2.2]
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| 9 || Sobol' indices for global sensitivity analysis || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt9/worksheet9.pdf Worksheet9] || June 28 || <!-- [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt9/ex1.1.py Assignment 2.1] [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt9/ex1.2.py Assignment 2.2]-->
 
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| 10 || Random fields in Uncertainty Quantification || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt10/worksheet10.pdf Worksheet10] || July 05 || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt10/ex1.py Assignment 1] [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt10/ex2.py Assignment 2]
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| 10 || Random fields in Uncertainty Quantification || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt10/worksheet10.pdf Worksheet10] || July 05 || <!-- [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt10/ex1.py Assignment 1] [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt10/ex2.py Assignment 2]-->
 
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| 11 || Software for Uncertainty Quantification || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt11/worksheet11.pdf Worksheet11] || July 12 || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt11/worksheet11_sol.pdf Solution worksheet11]
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| 11 || Software for Uncertainty Quantification || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt11/worksheet11.pdf Worksheet11] || July 12 || <!-- [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss17/blatt11/worksheet11_sol.pdf Solution worksheet11] -->
 
|}
 
|}
  

Latest revision as of 23:09, 14 May 2019

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