Ph.D. Course on Uncertainty Quantification
We offer a Ph.D. course on Uncertainty Quantification.
The course is offered with support from the DTU Compute Graduate School (ITMAN) and the Danish Center for Applied Mathematics and Mechanics (DCAMM) at Technical University of Denmark.
The aim of the course is to introduce the students to some of the methods and algorithms used in uncertainty quantification (UQ), and let the students experience these methods on elementary computer experiments.
The PhD course covers several topics in UQ: uncertainty parametrization, uncertainty propagation, sensitivity analysis, inference and uncertainty reduction. Related methods (e.g. Monte-Carlo simulation, spectral decompositions, surrogate modeling, Bayesian inference, Gaussian models) will be reviewed and some of them illustrated during computer experiments and projects. The objective is to give the student an overview of the "tools" available and how they can be modified for particular UQ applications.
Learning objectives:
A student who has met the objectives of the course will be able to:
- Understand problems and questions addressed by UQ methods.
- Understand how methods are used as building blocks to address UQ questions.
- Be able to choose a suitable method depending on the situation and problem.
- Implement some of these methods in C++.
- Skillfully perform numerical experiments and interpret the results.
- Perform sensitivity analyses and explain the behavior of the UQ methods.
- Identify and exploit the properties and structure of an uncertain model to select suitable approaches.
Requirements:
Basic course in numerical algorithms (e.g. 02601) and numerical analysis (e.g. 02685). It is considered an advantaged to have background in in advanced numerical methods course (e.g. 02689) and functional analysis.
The students must have a fundamental knowledge of numerical analysis and linear algebra and must be able to program. They are expected to read the first five chapters of the book before participating in the course.
Responsible:
The course will be given by:
- CNRS senior researcher Olivier Le Maitre (Laboratoire d'Informatique pour la Mechanique et les Sciences de l'Ingeneur (LIMSI), Paris, France),
