First Lecture
The first lecture will take place on Thursday, April 9th at 1:15 PM in room G50-H3. Further planning will be discussed there; please note that not all sessions will be held in person (see below). Specifically, there will be NO sessions on April 8th, 15th, 16th, and 17th!
Language
Course materials and exercise sheets are provided in both German and English. Click hier für die deutsche Version dieser Website.
General Information
The course Modeling, Simulation and Optimization (LSF) is offered during the summer semester for Bachelor's and Master's students at Otto von Guericke University Magdeburg. The content focuses on modeling optimization problems, particularly involving ordinary differential equations with applications in engineering. This course replaces Modeling 2 from the Mathematical Engineering program.
Downloads and Videos
PDF files of the lectures and exercises can be found on this password-protected page. Video recordings of the lectures are available here.
Current (Preliminary) Course Schedule
Note: This schedule is updated regularly. Even short-term changes will be communicated here. On Wednesday dates not listed below, no in-person sessions will take place.| Date | Attendance | Room | Content | Assignment |
|---|---|---|---|---|
| Thu, April 9 | BMI, MM, CoME | G50-H3 | 0. Organizational matters | ❌ |
| Fri, April 10 | BMI, MM, CoME | G50-H3 | 1. Introduction | ❌ |
| Thu, April 16 | ❌ | G50-H3 | Self-study, no in-person lecture | BMI, CoMe: Video 2 |
| Fri, April 17 | ❌ | G50-H3 | Self-study, no in-person lecture | ❌ |
| Thu, April 23 | BMI, MM, CoME | G50-H3 | 1. Introduction | BMI, MM, CoME: Sheet 1 |
| Fri, April 24 | BMI, MM, CoME | G50-H3 | 1. Introduction | ❌ |
| Wed, April 29 | BMI, MM, CoME | G40B-238 | Exercise Sheet 1 | BMI, MM, CoME: Sheet 2 |
| Thu, April 30 | ❌ | G50-H3 | Self-study, no in-person lecture | ❌ |
| Fri, May 1 | ❌ | G50-H3 | No in-person lecture (Public Holiday) | ❌ |
| Wed, May 6 | BMI, MM, CoME | G40B-238 | Exercise Sheet 2 | BMI: Sheet 3 |
| Thu, May 7 | BMI, CoME | G50-H3 | 2. Linear Programming | ❌ |
| Fri, May 8 | ❌ | G50-H3 | Self-study, no in-person lecture | BMI: Video 3 |
| Wed, May 13 | BMI | G40B-238 | Exercise Sheet 3 | ❌ |
| Thu, May 14 | ❌ | G50-H3 | Ascension Day (Public Holiday) | ❌ |
| Fri, May 15 | BMI | G50-H3 | 3. Nonlinear Programming | BMI, MM: Video 4 |
| Wed, May 13 | BMI, MM | G40B-238 | Exercise Sheet 4 | BMI, CoME: Sheet 4 |
| Thu, May 21 | BMI, MM | G50-H3 | 4. Function Evaluation and Derivatives / Simulation Methods Overview | ❌ |
| Fri, May 22 | BMI, MM, CoME | G50-H3 | 6. Optimization with Differential Equations | ❌ |
| Thu, May 28 | ❌ | G50-H3 | Self-study, no in-person session | ❌ |
| Fri, May 29 | ❌ | G50-H3 | Self-study, no in-person session | ❌ |
| Thu, June 4 | BMI, MM, CoME | G50-H3 | 6. Optimization with Differential Equations | ❌ |
| Fri, June 5 | BMI, MM, CoME | G50-H3 | 6. Optimization with Differential Equations | ❌ |
| Thu, June 11 | BMI, MM, CoME | G50-H3 | Written Exam | ❌ |
| Fri, June 12 | BMI, MM, CoME | G50-H3 | 5. Intro to Julia and Corleone.jl | BMI, MM, CoME: Sheet 5 |
| Wed, June 17 | BMI, MM, CoME | G40B-238 | Exercise Sheet 5 | ❌ |
| Thu, June 18 | BMI, MM, CoME | G50-H3 | 5. Intro to Julia and Corleone.jl | ❌ |
| Fri, June 19 | BMI, MM, CoME | G50-H3 | 5. Intro to Julia and Corleone.jl | ❌ |
| Thu, June 25 | BMI, MM, CoME | G50-H3 | 7. Case Studies | BMI, MM, CoME: Sheet 6 (case studies) |
| Fri, June 26 | BMI, MM, CoME | G50-H3 | 8. Learned Models | ❌ |
| Wed, July 1 | BMI, MM, CoME | G40B-238 | Consultation for Case Studies | ❌ |
| Thu, July 2 | BMI, MM, CoME | G50-H3 | 8. Learned Models | ❌ |
| Fri, July 3 | BMI, MM, CoME | G50-H3 | Final Presentations (Case Studies) | ❌ |
| Thu, July 9 | BMI, MM, CoME | G50-H3 | Final Presentations (Case Studies) | ❌ |
| Fri, July 10 | BMI, MM, CoME | G50-H3 | Final Presentations (Case Studies) | ❌ |
Target groups
This lectures addresses (at least) three curriculae and has modular and scalable contents:
| Curriculum | Presence | Study at home | Credits |
|---|---|---|---|
| BMI Mathematikingenieur (Bachelor) | 4SWS, 56h | 184h | 8 CPs |
| MM Mathematics (Master) | 4SWS, 56h | 124h | 6 CPs |
| CoME 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 | BMI | MM | CoME |
|---|---|---|---|---|
| 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 Julia and Corleone.jl | ✔ | ✔ | ✔ | ✔ |
| 6. Optimization with Differential Equations | ✔ | ✔ | ✔ | ✔ |
| 7. Case Studies | ✔ | ✔ | ✔ | ✔ |
| 8. Machine Learning and Hybrid Models | ✔ | ✔ | ✔ | ❌ |
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.
Exams
For all students in the curriculae Mathematics and Mathematikingenieur oral exams take place. Please make an individual appointment with the lecturer. For all CoME students, the confirmation of successful participation and the grade will be based on the performance in the written exam and in the case study presentation, as specified below.
Written exam
CoMe students need to write an exam in order to obtain a certificate of participation. The contents are selected from slides indicated with bell symbols of the chapters 1, 2, and 6. A focus will be on the formulation of optimization problems in different contexts, i.e., chapter 1 and the modeling aspects of chapters 2 and 6. Implementation (i.e., Julia or Corleone.jl) and algorithms will not be covered in detail.
Case study
All students need to present a case study. In addition, presentation slides and implementation code need to be submitted via email. You can work in teams of 2 to 4 students. CoME students will get a grade for their presentation, for students of mathematical curriculae a presentation is necessary to be admitted to an oral exam.
Questions?
Write to me: