Difference between revisions of "Algorithms for Uncertainty Quantification - Summer 18"

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| audience = Master students, e.g. of CSE, mathematics, informatics, data science, data engineering and analytics, physics,...
 
| audience = Master students, e.g. of CSE, mathematics, informatics, data science, data engineering and analytics, physics,...
 
| tutorials = [[Friedrich_Menhorn,_M.Sc._(hons)|Friedrich Menhorn]]
 
| tutorials = [[Friedrich_Menhorn,_M.Sc._(hons)|Friedrich Menhorn]]
| exam = preliminary: 01.08.2018, 11:00-12:15  
+
| exam = Location: 1450, Willy-Messerschmitt-Zeichensaal (5504.01.450)
 +
:Time: 01.08.2018, 11:00-12:15  
 
| tumonline = [https://campus.tum.de/tumonline/wbLv.wbShowLVDetail?pStpSpNr=950349357&pSpracheNr=2&pMUISuche=FALSE Algorithms for UQ] (IN2345)
 
| tumonline = [https://campus.tum.de/tumonline/wbLv.wbShowLVDetail?pStpSpNr=950349357&pSpracheNr=2&pMUISuche=FALSE Algorithms for UQ] (IN2345)
 
| moodle = tba
 
| moodle = tba
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== Announcements ==
 
== Announcements ==
 +
* <font color="red"> Review: 02.07.023, Aug 06, 2018, 12:00 - 12:45 </font color="red">
 
* <font color="red"> Decision on allowed exam material: No additional material needed/allowed! </font color="red">
 
* <font color="red"> Decision on allowed exam material: No additional material needed/allowed! </font color="red">
* <font color="red"> Old exam from summer 17 has been added to [https://www5.in.tum.de/wiki/index.php/Algorithms_for_Uncertainty_Quantification_-_Summer_18#Exam Exam] section </font color="red">
+
* <font color="black"> Old exam from summer 17 has been added to [https://www5.in.tum.de/wiki/index.php/Algorithms_for_Uncertainty_Quantification_-_Summer_18#Exam Exam] section </font color="black">
 
* <font color="black"> As announced in the tutorial we will swap lecture and tutorial in week 24. That means: Tutorial: June 12, 14:00-16:00; Lecture: June 13, 12:00-14:00.</font color="black">
 
* <font color="black"> As announced in the tutorial we will swap lecture and tutorial in week 24. That means: Tutorial: June 12, 14:00-16:00; Lecture: June 13, 12:00-14:00.</font color="black">
 
* <font color="black"> Evaluation of the lecture takes place during the lecture on June 13 2018. Please bring your laptop. </font color="black">
 
* <font color="black"> Evaluation of the lecture takes place during the lecture on June 13 2018. Please bring your laptop. </font color="black">
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! '''Number''' !! '''Topic''' !! '''Worksheet''' !! '''Tutorial''' !! '''Code''' !! '''Solution'''  
 
! '''Number''' !! '''Topic''' !! '''Worksheet''' !! '''Tutorial''' !! '''Code''' !! '''Solution'''  
 
|-
 
|-
| 1 || Python overview || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt1/worksheet1.pdf Worksheet1] || April 11 || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt1/ex.py Template] ||  [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt1/solution.pdf Solution 1] [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt1/assign2.py Solution 2] [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt1/sol.py Solution 3]
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| 1 || Python overview || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt1/worksheet1.pdf Worksheet1] || April 11 || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt1/ex.py Template] ||  <!-- [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt1/solution.pdf Solution 1] [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt1/assign2.py Solution 2] [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt1/sol.py Solution 3] -->
 
|-
 
|-
| 2 || Probability and statistics overview || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt2/worksheet2.pdf Worksheet2] || May 02 || || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt2/ex1.py Solution 1] [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt2/ex6.py Solution 6] [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt2/worksheet2_sol.pdf Solution.pdf]
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| 2 || Probability and statistics overview || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt2/worksheet2.pdf Worksheet2] || May 02 || || <!-- [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt2/ex1.py Solution 1] [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt2/ex6.py Solution 6] [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt2/worksheet2_sol.pdf Solution.pdf] -->
 
|-
 
|-
| 3 || Standard Monte Carlo sampling || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt3/worksheet3.pdf Worksheet3] || May 9 || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt3/Worksheet3.zip Template] || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt3/solution/ex2 Solution 2] [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt3/solution/ex3 Solution 3] [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt3/solution/ex4 Solution 4] [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt3/solution/ex5 Solution 5] [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt3/solution/worksheet3_sol.pdf Solution.pdf]
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| 3 || Standard Monte Carlo sampling || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt3/worksheet3.pdf Worksheet3] || May 9 || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt3/Worksheet3.zip Template] ||<!--  [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt3/solution/ex2 Solution 2] [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt3/solution/ex3 Solution 3] [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt3/solution/ex4 Solution 4] [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt3/solution/ex5 Solution 5] [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt3/solution/worksheet3_sol.pdf Solution.pdf] -->
 
|-
 
|-
| 4 || More advanced sampling techniques || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt4/worksheet4.pdf Worksheet4] || May 16 || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt4/Worksheet4.zip Template] ||  
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| 4 || More advanced sampling techniques || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt4/worksheet4.pdf Worksheet4] || May 16 || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt4/Worksheet4.zip Template] || <!--
 
[http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt4/solution/ex2.py Solution 2]  
 
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[http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt4/solution/ex3.2.py Solution 3.2]
[http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt4/solution/worksheet4_sol.pdf Solution.pdf]
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[http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt4/solution/worksheet4_sol.pdf Solution.pdf] -->
 
|-
 
|-
 
| 5 || Aspects of interpolation and quadrature || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt5/worksheet5.pdf Worksheet5] || May 30 || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt5/Worksheet5.zip Template] ||  
 
| 5 || Aspects of interpolation and quadrature || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt5/worksheet5.pdf Worksheet5] || May 30 || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt5/Worksheet5.zip Template] ||  
<!-- [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt5/solution/ex1a.py Solution 1 Legendre]
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[http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt5/solution/ex2_helper.py Helper 2] 
 
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[http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt5/solution/ex1.py Solution 1]   
 
[http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt5/solution/ex1.py Solution 1]   
 
[http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt5/solution/lebesgue_constant.py Solution 1 Optional]   
 
[http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt5/solution/lebesgue_constant.py Solution 1 Optional]   
 
[http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt5/solution/ex2.py Solution 2]   
 
[http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt5/solution/ex2.py Solution 2]   
[http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt5/solution/ex3.py Solution 3]
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[http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt5/solution/ex3.py Solution 3] -->
 
|-
 
|-
| 6 || Polynomial Chaos 1: the pseudo-spectral approach || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt6/worksheet6.pdf Worksheet6] || June 06 || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt6/Worksheet6.zip Template] ||  
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| 6 || Polynomial Chaos 1: the pseudo-spectral approach || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt6/worksheet6.pdf Worksheet6] || June 06 || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt6/Worksheet6.zip Template] || <!--
 
[http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt6/solution/ex1.py Solution 1]  
 
[http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt6/solution/ex1.py Solution 1]  
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[http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt6/solution/ex3a.py Helper 3]
 
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[http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt6/solution/ex3.py Solution 3]  
 
[http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt6/solution/ex3.py Solution 3]  
[http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt6/solution/worksheet6_sol.pdf Solution.pdf]
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|-
 
|-
 
| 7 || Polynomial Chaos 2: the stochastic Galerkin approach || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt7/worksheet7.pdf Worksheet7] || June 12 ||  ||
 
| 7 || Polynomial Chaos 2: the stochastic Galerkin approach || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt7/worksheet7.pdf Worksheet7] || June 12 ||  ||
[http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt7/solution/worksheet7_sol.pdf Solution.pdf]
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<!-- [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt7/solution/worksheet7_sol.pdf Solution.pdf] -->
 
|-
 
|-
| 8 || The sparse pseudo-spectral approach || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt8/worksheet8.pdf Worksheet8] || June 20 ||[http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt8/Worksheet8.zip Template] ||  
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| 8 || The sparse pseudo-spectral approach || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt8/worksheet8.pdf Worksheet8] || June 20 ||[http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt8/Worksheet8.zip Template] || <!--
 
[http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt8/solution/ex1.py Solution 1]  
 
[http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt8/solution/ex1.py Solution 1]  
[http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt8/solution/ex2.py Solution 2]  
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[http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt8/solution/ex2.py Solution 2] -->
 
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| 9 || Sobol' indices for global sensitivity analysis || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt9/worksheet9.pdf Worksheet9] || June 27 || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt9/ex2.py Ex2 Template] ||
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| 9 || Sobol' indices for global sensitivity analysis || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt9/worksheet9.pdf Worksheet9] || June 27 || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt9/ex2.py Ex2 Template] ||<!--
 
[http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt9/solution/worksheet9_sol.pdf Solution]
 
[http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt9/solution/worksheet9_sol.pdf Solution]
[http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt9/solution/ex2.1.py Solution 2]  
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| 10 || Random fields in Uncertainty Quantification || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt10/worksheet10.pdf Worksheet10] || July 04 || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt10/Worksheet10.zip Template] ||
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| 10 || Random fields in Uncertainty Quantification || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt10/worksheet10.pdf Worksheet10] || July 04 || [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt10/Worksheet10.zip Template] ||<!--
 
[http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt10/solution/ex1.py Solution 1]  
 
[http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt10/solution/ex1.py Solution 1]  
 
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|-
 
|-
| 11 || Software for Uncertainty Quantification & Old Exam|| [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt11/worksheet11.pdf Worksheet11] || July 11 || ||
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| 11 || Software for Uncertainty Quantification & Old Exam|| [http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt11/worksheet11.pdf Worksheet11] || July 11 || ||<!--
[http://www5.in.tum.de/lehre/vorlesungen/algo_uq/ss18/blatt11/worksheet11_sol.pdf Solution]
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= Exam =
 
= Exam =
<!--
+
 
 
* 2nd exam (check TUMonline):  
 
* 2nd exam (check TUMonline):  
** FRI, Oct 12, 10:30-11:45
+
** THU, Oct 11, 17:00-18:15
** room: MI lecture hall 2
+
** room: 00.06.011 (MI lecture hall 3)
** review session: THU, Oct 19, 15:00, room 02.05.053
+
** review session: t.b.a
-->
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* Review of first exam: 02.07.023, Aug 06, 2018, 12:00 - 12:45
 
* first exam (preliminary, check TUMonline):  
 
* first exam (preliminary, check TUMonline):  
 
** WED, Aug 01, 2018, 11:00-12:15 (75 min)
 
** WED, Aug 01, 2018, 11:00-12:15 (75 min)
 +
** room: 1450, Willy-Messerschmitt-Zeichensaal
 
<!--
 
<!--
** room: MI lecture hall 2
+
** Room: 1450, Willy-Messerschmitt-Zeichensaal
 
** review session: WED, Aug 30, 2017, 12:30 - 13:15, seminar room 02.07.023-->
 
** review session: WED, Aug 30, 2017, 12:30 - 13:15, seminar room 02.07.023-->
 
* covered topics (preliminary): everything except:
 
* covered topics (preliminary): everything except:

Latest revision as of 22:07, 14 May 2019

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
Location: 1450, Willy-Messerschmitt-Zeichensaal (5504.01.450)
Time: 01.08.2018, 11:00-12:15
Semesterwochenstunden / ECTS Credits
4 SWS (2V+2Ü) / 5 Credits
TUMonline
Algorithms for UQ (IN2345)



Announcements

  • Review: 02.07.023, Aug 06, 2018, 12:00 - 12:45
  • Decision on allowed exam material: No additional material needed/allowed!
  • Old exam from summer 17 has been added to Exam section
  • As announced in the tutorial we will swap lecture and tutorial in week 24. That means: Tutorial: June 12, 14:00-16:00; Lecture: June 13, 12:00-14:00.
  • Evaluation of the lecture takes place during the lecture on June 13 2018. Please bring your laptop.
  • Typos in the slides of §6 have been fixed. A print version of the slides is now also available
  • The first lecture takes place on April 10 2018.

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

Lecture Slides

Worksheets and Solutions

Number Topic Worksheet Tutorial Code Solution
1 Python overview Worksheet1 April 11 Template
2 Probability and statistics overview Worksheet2 May 02
3 Standard Monte Carlo sampling Worksheet3 May 9 Template
4 More advanced sampling techniques Worksheet4 May 16 Template
5 Aspects of interpolation and quadrature Worksheet5 May 30 Template
6 Polynomial Chaos 1: the pseudo-spectral approach Worksheet6 June 06 Template
7 Polynomial Chaos 2: the stochastic Galerkin approach Worksheet7 June 12
8 The sparse pseudo-spectral approach Worksheet8 June 20 Template
9 Sobol' indices for global sensitivity analysis Worksheet9 June 27 Ex2 Template
10 Random fields in Uncertainty Quantification Worksheet10 July 04 Template
11 Software for Uncertainty Quantification & Old Exam Worksheet11 July 11

Exam

  • 2nd exam (check TUMonline):
    • THU, Oct 11, 17:00-18:15
    • room: 00.06.011 (MI lecture hall 3)
    • review session: t.b.a
  • Review of first exam: 02.07.023, Aug 06, 2018, 12:00 - 12:45
  • first exam (preliminary, check TUMonline):
    • WED, Aug 01, 2018, 11:00-12:15 (75 min)
    • room: 1450, Willy-Messerschmitt-Zeichensaal
  • covered topics (preliminary): everything except:
    • inverse problems (lecture 12)
    • details of pure python programming
    • specific API of chaospy (or other packages)
  • style of exam exercises: similar to tutorials
  • allowed material: no material allowed
  • Written exam.

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