Allgemeine Angaben 

Algorithms for Uncertainty Quantification (IN2345)   




Vorlesung mit integrierten Übungen 












Zuordnungen: 1  
eLearning[Neuen MoodleKurs im aktuellen Semester bereitstellen] 



Angaben zur Abhaltung 

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 cuttingedge 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 HighPerformance 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 bruteforce approach • More advanced sampling methods: Quasi Monte Carlo & Co. • Relevant properties of interpolation & quadrature • 2nd class of algorithms: stochastic collocation via the pseudospectral approach: Is it possible to obtain accurate results with (much) less costs? • 3rd class of algorithms: stochastic Galerkin: Are we willing to (heavily) modify your software to gain accuracy? • Dimensionality reduction in UQ: apply hierarchical methodologies such as treebased 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, realworld measurements 




The students have an overview about methods in UQ, specifically for forward problems. Additionally, they gain insight about available software and possible applications. 




In this semester, we will include practical programming exercises into the tutorials. The programming language will be Python. These exercises are similar to homework, i.e. preparation beforehand is relevant, and will comprise approximately 50% of all tutorial exercises. 




Für die Anmeldung zur Teilnahme müssen Sie sich in TUMonline als Studierende*r identifizieren. 


Zusatzinformationen 

 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 




