Uncertainty Quantification  Show URL Convert to PDF XML representation

 

Modulcode: Inf-UncQu
Englische Bezeichnung: Uncertainty Quantification
Modulverantwortliche(r): Prof. Dr. Thomas Slawig
Turnus: unregelmäßig (WS16/17)
Präsenzzeiten: 4V 2Ü
ECTS: 9
Workload: 60 Std. Vorlesung, 30 Std. Präsenzübung, 150 Std. Selbststudium
Dauer: ein Semester
Modulkategorien: WI (BSc Inf. (15)) WI (MSc Inf (15)) MSc Math (Export)
Lehrsprache: Englisch

Kurzfassung:

Uncertainty Quantification (UQ) deals with the analysis of errosr and uncertainty propagation in simulation models. All kind of input parameters of models may be regarded as random variables, and their influence on the output variables or model results is studied. Numerical methods based on parameter estimation techniques are applied and implemented. Typical applications, e.g. from climate research, are studied.

Lernziele:

  • Understanding of uncertain quantities and processes in science and in simulation models
  • Knowledge and skills in parameter sensitivity studies and error propagation
  • Knowledge in important methods in uncertainty quantification and ability to apply them on exemplary simulation models
  • Kmowlegde in model order reduction
  • Implantation skills in the methods of UQ.

An additional focus is on theoretical aspects of numerical optimization methods, e.g. the proofs of important theorems or results.

Lehrinhalte:

  • Nature of uncertainties and errors
  • Applications
  • Prototypical models
  • Fundamentales of probability, random processes and statistics
  • Representation of random inputs
  • Parameter selection techniques
  • Freqentist and Bayesian techniques for parameter estimation
  • Uncertainty propagation in models
  • Surrogate models
  • Local and global sensitivity analysis

Voraussetzungen:

Knowledge and skills in analysis/calculus and linear algebra of a BSc program in mathematics, natural science, computer science, engineering or similar, programing skills in a higher language.

Prüfungsleistung:

Oral exam

Lehr- und Lernmethoden:

Lecture, presentations, written exercises, programming exercises, discussion

Verwendbarkeit:

MSc Mathematics, MSc Computational Science and Engineering, area Optimization and Optimal Control.

Literatur:

  • R Smith: Uncertainty Quantification: Theory, Implementation, and Applications (Computational Science and Engineering), Society of Industrial and Applied Mathematics, 2014.
  • T J Sullivan: Introduction to Uncertainty Quantification, Springer Texts in Applied Mathematics 63, 2015.
  • M G Morgan, M Henrion: Uncertainty - A Guide to Dealing with Uncertainty in Quantitative Risk and Policy Analysis, Cambridge University Press 1990
  • W L Oberkampf, C J Roy: Verification and Validation in Scientific Computing, Cambridge University Press 2010, online version at CAU library

Verweise:

Kommentar:

Lehrsprache Englisch, bei nur deutschsprachigen Teilnehmer*innen auf Wunsch Deutsch