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
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 fhe course's web page at:
https://luna.informatik.uni-mainz.de/mod1-22-23/
If you plan to participate in the lecture, please also make sure to sign up for the "mattermost" team using the instructions on that page.
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 |
|---|---|---|
| 10/25/2022 (Tuesday) | 14:00 - 16:00 | 04 432 2413 - Neubau Physik/Mathematik |
| 11/08/2022 (Tuesday) | 14:00 - 16:00 | 04 432 2413 - Neubau Physik/Mathematik |
| 11/15/2022 (Tuesday) | 14:00 - 16:00 | 04 432 2413 - Neubau Physik/Mathematik |
| 11/22/2022 (Tuesday) | 14:00 - 16:00 | 04 432 2413 - Neubau Physik/Mathematik |
| 11/29/2022 (Tuesday) | 14:00 - 16:00 | 04 432 2413 - Neubau Physik/Mathematik |
| 12/06/2022 (Tuesday) | 14:00 - 16:00 | 04 432 2413 - Neubau Physik/Mathematik |
| 12/13/2022 (Tuesday) | 14:00 - 16:00 | 04 432 2413 - Neubau Physik/Mathematik |
| 12/20/2022 (Tuesday) | 14:00 - 16:00 | 04 432 2413 - Neubau Physik/Mathematik |
| 01/10/2023 (Tuesday) | 14:00 - 16:00 | 04 432 2413 - Neubau Physik/Mathematik |
| 01/17/2023 (Tuesday) | 14:00 - 16:00 | 04 432 2413 - Neubau Physik/Mathematik |
| 01/24/2023 (Tuesday) | 14:00 - 16:00 | 04 432 2413 - Neubau Physik/Mathematik |
| 01/31/2023 (Tuesday) | 14:00 - 16:00 | 04 432 2413 - Neubau Physik/Mathematik |
| 02/07/2023 (Tuesday) | 14:00 - 16:00 | 04 432 2413 - Neubau Physik/Mathematik |