Modellreduktionsverfahren / Model Order Reduction Techniques in SS 2021

Prof. Dr. Martin Grepl ✉

News and Important Information

Dear students,
The official start of lectures for the summer term 2021 is April, 12. At this point it is not clear whether lectures are allowed to be held face-to-face or if we have to resort to video conferencing. However, given the current situation I assume that the lecture will most likely take place online.
We therefore proceed as follows:

• If you are interested in attending the course, please send me an email by noon on Friday, April 9, 2021.

• I will send out a doodle pool on Friday, April 9, in order to find a day/time for the first lecture.

• Lectures will then start most likely using video conferencing.

• I will discuss all necessary details in the first lecture (problem sets, recitations, ...).

Please also see the course information below concerning part 1 and 2 of the course.

Course information

• The course is split into two parts, Model Order Reduction Techniques 1 and 2, each with 2SWS lecture and 1 SWS exercises. Each part accounts for 5 credit points (ECTS).
• The first part will be held during the first half of the term, the second part during the second half. Students can take only part 1 (5 ECTS) or both parts (10 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