Language
All content of lecture and exercises will be available in English and German. Click here for the German version of this website.
General information
The lecture Modeling, Simulation and Optimization (LSF) addresses Bachelor and Master students of different curricula at Otto von Guericke Universität Magdeburg. The focus is on modeling optimization-related questions mainly involving ordinary differential equations with applications in the engineering sciences.
Downloads
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MatterMost Group
Registration and link to the channel.
Next lectures
There are two time slots for lectures and exercises in presence, Tuesday 11h15-12h45 (G03-214) and Thursday 15h15-16h45 (G03-214). Appointments in bold are in presence.
- Tuesday, 9. April: 0. Organisatorisches
- Thursday, 11. April: Study at home: Digital Twins in Oncology (see Material in owncloud directory)
- Tuesday, 16. April: 1. Introduction
- Thursday, 18. April: 1. Introduction Part 2
- Tuesday, 23. April: study at home, no event in presence!
- Thursday, 25. April: study at home, no event in presence!
- Tuesday, 30. April: study at home, no event in presence!
- Thursday, 2. May: study at home, no event in presence!
- Tuesday, 7. May: study at home, no event in presence!
- Thursday, 9. May: public holiday (Christi Himmelfahrt)
- Tuesday, 14. May: 2. Linear Programming and 3. Linear Programming and Exercise Sheet 1
Target groups
This lectures addresses (at least) three curriculae and has modular and scalable contents:
| Curriculum | Presence | Study at home | Credits |
|---|---|---|---|
| I Mathematikingenieur (Bachelor) | 4SWS, 56h | 184h | 8 CPs |
| II Mathematics (Master) | 4SWS, 56h | 124h | 6 CPs |
| III Comp. Methods for Engineering (Master) | 4SWS, 56h | 94h | 5 CPs |
Contents
The content revolves around the modeling of optimization problems, especially in ordinary differential equations, with applications from engineering sciences. Different levels of prior knowledge and requirements of the addressed courses are accommodated through a modular approach and varying levels of self-study demands. Some content serves as review for certain students (especially those in the Mathematics Master's program), while more detailed topics, as well as certain contents, are offered only in the inverted classroom format. Table of contents and chapter assignments for the programs are provided.
| Chapter | Presence | I | II | III |
|---|---|---|---|---|
| 1. Introduction and Examples of Modeling Dynamic Processes | ✔ | ✔ | ✔ | ✔ |
| 2. Overview Linear Optimization: Formulation, Optimality Conditions, Algorithms | ❌ | ✔ | ❌ | ✔ |
| 3. Overview Nonlinear Optimization: Formulation, Optimality Conditions, Algorithms | ❌ | ✔ | ❌ | ❌ |
| 4. Overview Simulation Methods | ❌ | ✔ | ✔ | ❌ |
| 5. Introduction to Python and CasADi | ✔ | ✔ | ❌ | ✔ |
| 6. Optimization with Differential Equations | ❌ | ✔ | ✔ | ✔ |
| 7. Case Studies | ✔ | ✔ | ✔ | ✔ |
| 8. Machine Learning and Hybrid Models (Details: ICF) | ❌ | ✔ | ✔ | ❌ |
During the presence time, alongside lectures, exercises ranging from 1 to 2 weekly hours (SWS) will be integrated. The objective, besides mathematical tasks, will be to familiarize students with modern modeling and optimization tools. When examining case studies, students' own problem formulations will be incorporated.
Goals and competences
The students acquire expertise in mathematical modeling of engineering problems, focusing on modeling with differential equations and the interactions between modeling on one side and simulation and optimization on the other. An overview of elementary algorithmic techniques is provided, including parameter estimation and experimental design for dynamic systems, as well as regarding optimality conditions and algorithms for nonlinear, derivative-based optimal control, i.e., optimization with underlying differential equations. In addition to modeling the underlying physical, biological, or chemical processes, the modeling of constraints and objective functions and their impact on algorithmics, complexity, and results are discussed.
In accompanying exercises, students deepen their understanding and learn to efficiently implement algorithms on the computer and apply them to specific problem scenarios.
Questions?
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