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2023/2024
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Non-Stochastic Methods for Uncertainty Quantification

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Code Completion Credits Range Language
D01NSM_EN ZK 2P English
Garant předmětu:
Jan Chleboun
Lecturer:
Jan Chleboun
Tutor:
Supervisor:
Department of Mathematics
Synopsis:

The goal is to make students familiar with some non-stochastic methods for uncertainty quantification. Uncertainty is considered in parameters entering mathematical models. Consequently, the model output represented by a quantity of interest is also uncertain and this uncertainty is to be assessed.

Topics: Aleatoric and epistemic uncertainty. Differential equations with uncertain data. Various approaches to uncertainty quantification. The worst- and best-case scenario method.

Elements of fuzzy set theory (membership function, alpha-cut, Zadeh’s extension principle). Fuzzification, various definitions of membership functions, a connection to information gap theory by Y. Ben-Haim. An introduction to the Dempster-Shafer theory (DST), belief and plauzibility, Dempster’s rule of combination. Probabilistic interpretation of DST. Application to engineering problems with uncertain data and a non-trivial state problem. Tools for solving such problems – minimization algorithms, sensitivity analysis, finite element method.

Requirements:
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Time-table for winter semester 2023/2024:
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Time-table for summer semester 2023/2024:
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The course is a part of the following study plans:
Data valid to 2024-06-12
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