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Stochastic Methods for Engineers and Natural Scientists
Last Updated: 2026-02-05 15:48:07
Abstract
The course provides an introduction into stochastic methods that are applicable for example for the description and modeling of turbulent and subsurface flows. Moreover, mathematical techniques are presented that are used to quantify uncertainty in various engineering applications.
Objective
By the end of the course you should be able to mathematically describe random quantities and their effect on physical systems. Moreover, you should be able to develop basic stochastic models of such systems.
Content
- Probability theory, single and multiple random variables, mappings of random variables - Estimation of statistical moments and probability densities based on data - Stochastic differential equations, Ito calculus, PDF evolution equations - Monte Carlo integration with importance and stratified sampling - Markov-chain Monte Carlo sampling - Control-variate and multi-level Monte Carlo estimation All topics are illustrated with engineering applications.
Resources
Lecture Notes
Detailed lecture notes will be provided.
Literature
Some textbooks related to the material covered in the course: Stochastic Methods: A Handbook for the Natural and Social Sciences, Crispin Gardiner, Springer, 2010 The Fokker-Planck Equation: Methods of Solutions and Applications, Hannes Risken, Springer, 1996 Turbulent Flows, S.B. Pope, Cambridge University Press, 2000 Spectral Methods for Uncertainty Quantification, O.P. Le Maitre and O.M. Knio, Springer, 2010
General Information
- Language
- English
- Levels
- BSC , MSC
- Frequency
- Yearly recurring
Examination
- Type
- session examination
- Mode
- written 60 minutes
- Aids
- no aides are allowed
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture with exercise |
Stochastic Methods for Engineers and Natural Scientists
Lecture: 10-12
Exercises: 12-14
|
|
4 h weekly |
Offered In
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Electives (In the ‘electives’ subcategory, at least two course units must be successfully completed.)
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Energy, Flows and Processes (The courses listed in this category “Core Courses” are recommended. Alternative courses can be chosen in agreement with the tutor.)
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Electives (In the ‘electives’ subcategory, at least two course units must be successfully completed.)
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