Model Order Reduction
Model Order Reduction (MOR) is the art of reducing a system's complexity while preserving its input-output behavior as much as possible.
Processes in all fields of todays technological world, like physics, chemistry and electronics, but also in finance, are very often described by dynamical systems. With the help of these dynamical systems, computer simulations, i.e. virtual experiments, are carried out. In this way, new products can be designed without having to build costly prototyps.
Due to the demand of more and more realistic simulations, the dynamical systems, i.e., the mathematical models, have to reflect more and more details of the real world problem. By this, the models' dimensions are increasing and simulations can often be carried out at high computational cost only.
In the design process, however, results are needed quickly. In circuit design, e.g., structures may need to be changed or parameters may need to be altered, in order to satisfy design rules or meet the prescribed performance. One cannot afford idle time, waiting for long simulation runs to be ready.
Model Order Reduction allows to speed up simulations in cases where one is not interested in all details of a system but merely in its input-output behavior. That means, considering a system, one may ask:
- How do varying parameters influence certain performances ?
Using the example of circuit design: How do widths and lengths of transistor channels, e.g., influence the voltage gain of a circuit. - Is a system stable?
Using the example of circuit design: In which frequency range, e.g., of voltage sources, does the circuit perform as expected - How do coupled subproblems interact?
Using the example of circuit design: How are signals applied at input-terminals translated to output-pins?
Classical situations in circuit design, where one does not need to know internals of blocks are optimization of design parameters (widths, lengths, ...) and post layout simulations and full system verifications. In the latter two cases, systems of coupled models are considered. In post layout simulations one has to deal with artificial, parasitic circuits, describing wiring effects.
Model Order Reduction automatically captures the essential features of a structure, omitting information which are not decisive for the answer to the above questions. Model Order reduction replaces in this way a dynamical system with another dynamical system producing (almost) the same output, given the same input with less internal states.
MOR replaces high dimensional (e.g. millions of degrees of freedom) with low dimensional (e.g. a hundred of degrees of freedom ) problems, that are then used instead in the numerical simulation.
The working group "Applied Mathematics/Numerical Analysis" has gathered expertise in MOR, especially in circuit design. Within the EU-Marie Curie Initial Training Network COMSON, attention was concentrated on MOR for Differential Algebraic Equations. Members that have been working on MOR in the EU-Marie Curie Transfer of Knowledge project O-MOORE-NICE! gathered knowledge especially in the still immature field of MOR for nonlinear problems.
Current research topics include:
- MOR for nonlinear, parameterized problems
- structure preserving MOR
- MOR for Differential Algebraic Equations
- MOR in financial applications, i.e., option prizing
Group members working on that field
- Jan ter Maten
- Roland Pulch
Publications
- 2024
4912.
Göstl, Robert; Storch, Sonja
Trendbericht Makromolekulare Chemie 2024
Nachrichten aus der Chemie, 72 (10) :52-59
October 20244911.
Kunz, K.; Springer, Bastian L.; Klahn, Philipp; Aldemir, Hülya; Mohr, Fabian; Kirsch, S. F.
Synthesis of N2-Substituted 1,2,3-Triazoles
Organic Letters, 2024
October 2024
Publisher: ACS4910.
Broschinski, Christian; Majer, Felix; He, Siyang; Kuehne, Alexander J. C.; Göstl, Robert
Mechanochemical Activation of Red-Light-Excited Triplet–Triplet Annihilation Photon Upconversion
ACS Applied Optical Materials, 2 (9) :1764–1769
September 20244909.
[german] Gökkus, Yasemin; Gutenberg, Janna; Kiesling, Elisabeth; Kremer, Richard; Wernicke, Anne; Bohrmann-Linde, Claudia
Sprachsensibler Chemieunterricht digital umgesetzt – Ein Seminarexkurs im Rahmen des Praxissemesters
DiMawe – Zeitschrift für Konzepte und Arbeitsmaterialien für Lehrer*innenbildung und Unterricht, 6 (1)
September 20244908.
Tapera, Michael; Chotia, Mohit; Mayer-Figge, Jan Lukas; Gómez-Suárez, Adrián; Kirsch, S. F.
anti-Dihydroxylation of olefins enabled by in situ generated peroxyacetic acid
Green Chemistry, 2024
09 2024
Publisher: RCS
ISSN: 1463-92704907.
[English] Schrader, Claudia; Diekmann, Charlotte; Schulz, Paulina; Mack, Nils; Bohrmann, Claudia; Zeller, Diana
Hands-on training: Effects on virtual presence, learning-centered emotions, cognitive load and learning outcome when learning with virtual reality
Computers in Human Behavior Reports (100487)
09 20244906.
[german] Zeller, Diana; Bohrmann-Linde, Claudia; Diekmann, Charlotte; Mack, Nils; Schrader, Claudia
Die Teilchenebene in 3D erkunden – Potenziale und Herausforderungen von Virtual Reality im Unterricht
Unterricht Chemie, 202/203 :80-85
September 20244905.
[german] Kiesling, Elisabeth; Bohrmann-Linde, Claudia
What to do with CO2? – Eine bilinguale Schülerlaboreinheit als Beitrag zu BNE
Unterricht Chemie, 202/203 :86-91
September 20244904.
[german] Cornelius, Soraya; Bohrmann-Linde, Claudia
Der Fleck muss weg! – Mit Selbstlernbüchern digitale Lernumgebungen zum Kompetenzerwerb für die Produktion eines Erklärvideos schaffen
Unterricht Chemie, 202/203 :56-61
September 20244903.
[german] Zeller, Diana; Grandrath, Rebecca
Eigene interaktive Lernbücher gestalten – Ein Überblick für die Produktion mit Book Creator und Pages
Unterricht Chemie, 202/203 :8-13
September 20244902.
[german] Zeller, Diana
Schritt für Schritt zum digitalen Versuchsprotokoll – Digitale Lernumgebungen mit Miro umsetzen
Unterricht Chemie, 202/203 :27-31
September 20244901.
[german] Zeller, Diana; Bohrmann-Linde, Claudia; Wlotzka, Petra
Selbstgesteuert und selbstorganisiert lernen – Digitale Lernumgebungen für den Chemieunterricht gestalten und einsetzen
Unterricht Chemie, 202/203 :2-7
September 20244900.
[german] Hüsken, Daniel; Meuter, Nico
Galvanische Zellen erkunden – Eine ergänzende Lernumgebung zur Einführung in die elektrochemische Spannungsreihe
Unterricht Chemie, 202/203 :68-73
September 20244899.
Ishaqat, Aman; Hahmann, Johannes; Lin, Cheng; Zhang, Xiaofeng; He, Chuanjiang; Rath, Wolfgang H.; Habib, Pardes; Sahnoun, Sabri E. M.; Rahimi, Khosrow; Vinokur, Rostislav; Mottaghy, Felix M.; Göstl, Robert; Bartneck, Matthias; Herrmann, Andreas
In Vivo Polymer Mechanochemistry with Polynucleotides
Advanced Materials, 36 (32) :2403752
August 2024
ISSN: 1521-40954898.
Fan, Jilin; Xuan, Mingjun; Zhang, Kuan; Vinokur, Rostislav; Zheng, Lifei; Göstl, Robert; Herrmann, Andreas
Accelerated Mechanophore Activation and Drug Release in Network Core-Structured Star Polymers Using High-Intensity Focused Ultrasound
Small Science, 4 (8) :2400082
August 20244897.
Fan, Jilin; Zhang, Kuan; Xuan, Mingjun; Gao, Xiang; Vinokur, Rostislav; Göstl, Robert; Zheng, Lifei; Herrmann, Andreas
High-Intensity Focused Ultrasound-Induced Disulfide Mechanophore Activation in Polymeric Nanostructures for Molecule Release
CCS Chemistry, 6 (8) :1895-1907
August 20244896.
Tapera, Michael; Borghi, Federica; Mayer-Figge, Jan Lukas; Mittendorf, Fabia; Celik, I. E.; Gómez-Suárez, Adrián; Kirsch, S. F.
A Formal Synthesis of (+)-Hannokinol Using a Chiral Horner–Wittig Reagent
Molecules, 29 :3710
07 2024
Publisher: MDPI
ISSN: 1420-30494895.
Alcalde, Albert; Fantuzzi, Giovanni; Zuazua, Enrique
Clustering in pure-attention hardmax transformers and its role in sentiment analysis
06 20244894.
Ballaschk, Frederic; Bensberg, Kathrin; Crone, Benedikt; Kirsch, S. F.; Menz, Helge
Synthesis of the monomeric counterpart of Marinomycin A and B
Organic & Biomolecular Chemistry, 2024
06 2024
Publisher: RSC4893.
Xu, Zhuo; Tucsnak, Marius
LQR control for a system describing the interaction between a floating solid and the surrounding fluid
06 20244892.
Glück, Jochen; Mui, Jonathan
Non-positivity of the heat equation with non-local Robin boundary conditions
04 20244891.
Aydonat, Simay; Hergesell, Adrian H.; Seitzinger, Claire L.; Lennarz, Regina; Chang, George; Sievers, Carsten; Meisner, Jan; Vollmer, Ina; Göstl, Robert
Leveraging mechanochemistry for sustainable polymer degradation
Polymer Journal, 56 (4) :249-268
April 2024
ISSN: 1349-05404890.
Rath, Wolfgang H.; Göstl, Robert; Herrmann, Andreas
Mechanochemical Activation of DNAzyme by Ultrasound
Advanced Science, 11 (8) :2306236
February 2024
ISSN: 2198-38444889.
[german] Tausch, Michael W.
Curriculare Innovation - Ein Imperativ für den Chemieunterricht
Volume Chemie professionell unterrichten
Publisher: T. Palenta
February 2024ISBN: 9783758478413
4888.
Celik, I. E.; Mittendorf, Fabia; Gómez-Suárez, Adrián; Kirsch, S. F.
Formal synthesis of bastimolide A using a chiral Horner-Wittig reagent and a bifunctional aldehyde as key building blocks
Tetrahedron Chem, 9
02 2024
Publisher: Elsevier
ISSN: 2666-951X