151-0709-00L Stochastic Methods for Engineers and Natural Scientists
| Semester | Autumn Semester 2023 |
| Lecturers | D. W. Meyer-Massetti |
| Periodicity | yearly recurring course |
| Language of instruction | English |
| 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. | ||||||||||||||||||||||||||||||
| Learning 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 - Statistical tests for means and goodness-of-fit All topics are illustrated with engineering applications. | ||||||||||||||||||||||||||||||
| 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 | ||||||||||||||||||||||||||||||
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