Model Reduction for Dynamical Systems (Summer Semester 2023)
This course deals with Model Order Reduction (MOR) for the efficient simulation, analysis, control, and optimization of large-scale dynamical systems. A large variety of MOR methods will be introduced and discussed, including both frequency-domain and time-domain methods. MOR methods applied to real-world problems will be presented in order to highlight the necessity and usefulness of model reduction.
Contents - Schedule - Certification - Lectures - Exercises - Homework - References
- Basics of Linear Systems and Control Theory
- Singular Value Decomposition
- Input and Output Dynamical Systems
- Frequency Domain Behavior and Transfer Functions
- Gramians and Energy Functionals
- System-theoretic Model Reduction
- Balanced Truncation
- Pade Approximation
- Interpolation-based Model Reduction
- Model Reduction of Nonlinear Systems
- Proper Orthogonal Decomposition (POD)
- Discrete Empirical Interpolation Method (DEIM)
- Model Reduction of Parametric Systems
- Multi-moment Matching
- Reduced Basis (RB) Method
- Data-Driven Methods for Dynamical Systems
- Eigenvalue Realization Algorithm (ERA)
- Loewner Framework
- Dynamic Mode Decomposition
- Operator Inference
The content of this lecture is summarized in the follwoing slides.
Certificate for successful participation
Will be announced in the lecture
- Week 1 (12/04 and 14/04):
- A.C. Antoulas: Approximation of Large-Scale Dynamical Systems, SIAM, Philadelphia, 2005.
- A. C. Athanasios, C. A. Beattie, S. Gugercin: Interpolatory Methods for Model Reduction, SIAM, 2020.
- P. Benner, M. Ohlberger, A. Cohen, K. Willcox: Model Reduction and Approximation: Theory and Algorithms, SIAM, 2017.
- Lecture notes from Dr. Matthias Voigt