Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Module MAT-81-38-M-7

Uncertainty Quantification (M, 4.5 LP)

Module Identification

Module Number Module Name CP (Effort)
MAT-81-38-M-7 Uncertainty Quantification 4.5 CP (135 h)

Basedata

CP, Effort 4.5 CP = 135 h
Position of the semester 1 Sem. irreg.
Level [7] Master (Advanced)
Language [EN] English
Module Manager
Lecturers
+ further Lecturers of the department Mathematics
Area of study [MAT-TEMA] Industrial Mathematics
Reference course of study [MAT-88.105-SG] M.Sc. Mathematics
Livecycle-State [NORM] Active

Courses

Type/SWS Course Number Title Choice in
Module-Part
Presence-Time /
Self-Study
SL SL is
required for exa.
PL CP Sem.
2V MAT-81-38-K-7
Uncertainty Quantification
P 28 h 107 h - - PL1 4.5 irreg.
  • About [MAT-81-38-K-7]: Title: "Uncertainty Quantification"; Presence-Time: 28 h; Self-Study: 107 h

Examination achievement PL1

  • Form of examination: oral examination (20-30 Min.)
  • Examination Frequency: irregular (by arrangement)
  • Examination number: 86460 ("Uncertainty Quantification")

Evaluation of grades

The grade of the module examination is also the module grade.


Contents

  • introduction: prototypical models,
  • basic concepts from probability and approximation theory: random vectors, orthogonal polynomials,
  • representation of random inputs: independent and correlated random inputs, Karhunen-Loève expansion,
  • propagation of random inputs: (Multilevel) Monte-Carlo methods, stochastic Galerkin methods, stochastic collocation.

Competencies / intended learning achievements

Upon successful completion of this module, the students have studied and understood advanced mathematical methods handling systems with stochastic parameters, in particular, of systems which are described by ordinary or partial differential equations. They understand the basic approach to uncertainty quantification and are familiar with the propagation of random inputs. They are able to critically apply the techniques learnt during the lecture to study practical problems which can be modeled with perturbed stochastic differential equations. They are able to name and to prove the essential propositions of the lecture as well as to classify and to explain the connections.

Literature

  • R.C. Smith: Uncertainty Quantification,
  • R. Abgrall, S. Mishra: Uncertainty Quantification for Hyperbolic Conservation Laws.

References to Module / Module Number [MAT-81-38-M-7]

Module-Pool Name
[MAT-8x-MPOOL-7] Specialisation Modelling and Scientific Computing (M.Sc.)
[MAT-AM-MPOOL-7] Applied Mathematics (Advanced Modules M.Sc.)