## 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 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).

### 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 |
---|---|---|

04/15/2024 (Monday) | 12:15 - 13:45 | 04 224 2413 - Neubau Physik/Mathematik |

04/22/2024 (Monday) | 12:15 - 13:45 | 04 224 2413 - Neubau Physik/Mathematik |

04/29/2024 (Monday) | 12:15 - 13:45 | 04 224 2413 - Neubau Physik/Mathematik |

05/06/2024 (Monday) | 12:15 - 13:45 | 04 224 2413 - Neubau Physik/Mathematik |

05/13/2024 (Monday) | 12:15 - 13:45 | 04 224 2413 - Neubau Physik/Mathematik |

05/27/2024 (Monday) | 12:15 - 13:45 | 04 224 2413 - Neubau Physik/Mathematik |

06/03/2024 (Monday) | 12:15 - 13:45 | 04 224 2413 - Neubau Physik/Mathematik |

06/10/2024 (Monday) | 12:15 - 13:45 | 04 224 2413 - Neubau Physik/Mathematik |

06/17/2024 (Monday) | 12:15 - 13:45 | 04 224 2413 - Neubau Physik/Mathematik |

06/24/2024 (Monday) | 12:15 - 13:45 | 04 224 2413 - Neubau Physik/Mathematik |

07/01/2024 (Monday) | 12:15 - 13:45 | 04 224 2413 - Neubau Physik/Mathematik |

07/08/2024 (Monday) | 12:15 - 13:45 | 04 224 2413 - Neubau Physik/Mathematik |

07/15/2024 (Monday) | 12:15 - 13:45 | 04 224 2413 - Neubau Physik/Mathematik |