- 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.
Uncertainty Quantification (M, 4.5 LP)
|Module Number||Module Name||CP (Effort)|
|MAT-81-38-M-7||Uncertainty Quantification||4.5 CP (135 h)|
|CP, Effort||4.5 CP = 135 h|
|Position of the semester||1 Sem. irreg.|
|Level|| Master (Advanced)|
+ further Lecturers of the department Mathematics
|Area of study||[MAT-TEMA] Industrial Mathematics|
|Reference course of study||[MAT-88.105-SG] M.Sc. Mathematics|
|Type/SWS||Course Number||Title||Choice in |
|SL||SL is |
required for exa.
|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.
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.
- R.C. Smith: Uncertainty Quantification,
- R. Abgrall, S. Mishra: Uncertainty Quantification for Hyperbolic Conservation Laws.
Requirements for attendance of the module (informal)
- [MAT-10-1-M-2] Fundamentals of Mathematics (M, 28.0 LP)
- [MAT-14-11-M-3] Introduction to Numerical Methods (M, 9.0 LP)
- [MAT-14-14-M-3] Stochastic Methods (M, 9.0 LP)
- [MAT-80-11B-M-4] Introduction to PDE (M, 4.5 LP)