Model Order Reduction Techniques (Modellreduktionsverfahren)
Dates
Course |
Date |
Note |
|---|---|---|
| Lecture | TBD (see info below) | Room 224.3 (main building) |
| Tutorial | TBD |
News and Important Information
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The first meeting will take place on Monday, Oct 10, at 12:30pm in room 224.3 in the main building (Templergraben 55).
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If you are interested in attending the course but cannot attend the first meeting, please send me an email by Thursday, October 10.
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All necessary details will be discussed in the first lecture (course schedule, problem sets, recitations, ...).
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Regular classes will start in the second week of lectures.
Please also see the course information below concerning part 1 and 2 of the course.
Course information
- This module (5 ECTS) has 2 hours lecture and 1 hours recitation/exercise per week. The recitations will be held approximately every 2 weeks. There will be a second part of this module, Model Order Reduction Techniques 2, which will be offered in the summer term 2025 (also 5 ECTS).
- The problem sets will require some programming in Matlab.
Content
The focus of this course is on model order reduction methods for large-scale systems. These systems typically arise when partial differential equations are solved using numerical methods such as the finite element method. Model order reduction techniques provide an efficient and reliable way of solving these problems in the many-query or real-time context, such as optimization, characterization, and control.
We first present reduced basis approximations and associated a posteriori error estimation procedures for rapid and reliable solution of parametrized partial differential equations (PDEs). The focus is on rapidly convergent Galerkin approximations on a space spanned by "snapshots" on the parametrically induced solution manifold; rigorous and sharp a posteriori error estimators for the outputs/quantities of interest; efficient selection of quasi-optimal samples in general parameter domains; and Offline-Online computational procedures for rapid calculation in the many-query and real-time contexts. We subsequently consider Proper Orthogonal Decomposition (POD) and Balanced Truncation for the approximation of systems which only depend on time.
Lecture notes and additional literature
The notes and slides from the lecture are the primary source for the class. The following references cover some of the topics or provide further reading:
- A.T. Patera and G. Rozza, Reduced Basis Approximation and A Posteriori Error Estimation for Parametrized Partial Differential Equations. Version 1.0, Copyright MIT 2006-2007, to appear in (tentative rubric) MIT Pappalardo Graduate Monographs in Mechanical Engineering.
- A.C. Antoulas, Approximation of Large-Scale Dynamical Systems (Advances in Design and Control). SIAM, 2005.
- Additional reference for the general preliminaries: lecture notes on FEM from the class 16.920 Numerical Methods for PDEs . (links to Notes 1, Notes 2, Notes 3, Notes 4)
- Additional reference for SVD and POD: lecture notes by Prof. S. Volkwein, Uni Konstanz (link to Script)
- Further texts may be added during the term.
Lecture slides and notes (will be posted before each lecture)
- See RWTH Moodle
Assignments
- See RWTH Moodle