Modellierung I
Instructors: Univ.-Prof. Dr. Michael WandShortname: 08.079.314
Course No.: 08.079.314
Course Type: Vorlesung/Übung
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.
Digital teaching
We are planning to offer the course in a "blended-learning" format, which includes prerecorded videos in combination with on-site meetings in person.More information is available on the course's web page at:
https://luna.informatik.uni-mainz.de/mod1-26/
(available since March 31 2026)
Recommended reading list
Will be announced during the lecture.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.
Dates
| Date (Day of the week) | Time | Location |
|---|---|---|
| 04/13/2026 (Monday) | 12:15 - 13:45 | 04 432 2413 - Neubau Physik/Mathematik |
| 04/20/2026 (Monday) | 12:15 - 13:45 | 04 432 2413 - Neubau Physik/Mathematik |
| 04/27/2026 (Monday) | 12:15 - 13:45 | 04 432 2413 - Neubau Physik/Mathematik |
| 05/04/2026 (Monday) | 12:15 - 13:45 | 04 432 2413 - Neubau Physik/Mathematik |
| 05/11/2026 (Monday) | 12:15 - 13:45 | 04 432 2413 - Neubau Physik/Mathematik |
| 05/18/2026 (Monday) | 12:15 - 13:45 | 04 432 2413 - Neubau Physik/Mathematik |
| 06/01/2026 (Monday) | 12:15 - 13:45 | 04 432 2413 - Neubau Physik/Mathematik |
| 06/08/2026 (Monday) | 12:15 - 13:45 | 04 432 2413 - Neubau Physik/Mathematik |
| 06/15/2026 (Monday) | 12:15 - 13:45 | 04 432 2413 - Neubau Physik/Mathematik |
| 06/22/2026 (Monday) | 12:15 - 13:45 | 04 432 2413 - Neubau Physik/Mathematik |
| 06/29/2026 (Monday) | 12:15 - 13:45 | 04 432 2413 - Neubau Physik/Mathematik |
| 07/06/2026 (Monday) | 12:15 - 13:45 | 04 432 2413 - Neubau Physik/Mathematik |