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Instructors: Univ.-Prof. Dr. Michael Wand
Event type:
Lecture/practice class
Displayed in timetable as:
08.079.314
Hours per week:
4
Credits:
6,0
Language of instruction:
German
Min. | Max. participants:
- | -
Requirements / organisational issues:
The lecture requires a good background in mathematics (optimal: Math or Physics as minor subject) and some programming skills (Python and/or -optionally- C++) as well as basic knowledge of algorithms and data structures (e.g. lecture "Datenstrukturen und effiziente Algorithmen").
We will make use of quite some computer graphics for visualization; it is useful to have some knowledge of 3D computer graphics, but this is not required.
Contents:
The lecture discusses basic concepts of how to model real-world phenomena with a computer. The goal is to give an overview of basic mathematical and theoretical tools for modeling, and (in particular) to bring these concepts into practical implementation and application.
Modeling of real-world phenomena poses a number of questions:
- Representation: Which information is constitutes the state of the modeled phenomenon?
- Rules/dynamics: How does the phenomenon evolve/behave over time / space?
- Simulation: How can we simulate it?
- Inverse problems: Can we adjust the model parameter such that the simulation explains real-world measurement data?
- Variational modeling and optimization: How can we model problems implicitly through the use of objective functions and constraints?
Bottom Line: Modeling 1 = Linear Modelling
Modelling 1 focusses on linear models (model state is a vector in a linear space). It will discuss representations and sampling issues, and show a number of practical examples (such as global illumination or dynamics of objects). For optimization and inverse problems, we consider simple quadratic variational formulations that can be solved with the nice & easy to use linear algebra tools.
Recommended reading list:
Will be announced during the lecture.
Digital teaching:
The course will be offered in a blended-learning format, which includes on-site meetings in person. This might change according to circumstances.
Up-to-date information is available via the course's web page at:
https://luna.informatik.uni-mainz.de/mod1-24/
(available 04/2024)
Important: Please sign up for our electronic discussion board, as explained on the webpage, before the lecture starts (i.e., early April 2024).
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