Applied and Computational Mathematics (ACM)

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



2022

6124.

[german] Kremer, Richard; Bohrmann-Linde, Claudia; Tausch, Michael W.
Künstliche Photosynthese im Fokus - Photokatalytische Wasserstofferzeugung in der Eintopfzelle
CHEMKON, 29 (6) :646-653
September 2022

6123.

[german] Bohrmann-Linde, Claudia; Gökkus, Yasemin; Humbert, Ludger; Kiesling, Elisabeth; Kremer, Richard; Losch, Daniel; Schmitz, Denise; Zeller, Diana
Analyse, Struktur und Darstellung chemiedidaktischer Elemente aus informatischer Perspektive – Entwicklung eines interdisziplinären Lehrkonzeptes
MNU-Journal, 05.2022 :423-429
September 2022

6122.

Bohrmann-Linde, Claudia; Siehr, Ilona
CHEMIE Einführungsphase Nordrhein-Westfalen
Herausgeber: C.C.Buchner Verlag, Bamberg
August 2022

ISBN: 9783661060019

6121.

[german] Monique, Meier; Zeller, Diana; Stinken-Rösner, Lisa
Interaktive Videoformate für den naturwissenschaftlichen Unterricht. Vom Rezipieren zum Interagieren
Unterricht Biologie, 475 :44-47
07 2022

6120.

[german] Grandrath, Rebecca; Bohrmann-Linde, Claudia
Strom aus Bäckerhefe
Nachrichten aus der Chemie, 70 (7-8) :18-21
Juli 2022

6119.

[german] Grandrath, Rebecca; Bohrmann-Linde, Claudia
Entwicklung eines lowcost Experiments für den Chemieunterricht am Beispiel der enzymatischen Brennstoffzelle mit Lactase
CHEMKON, 29 (S1) :233-238
Juni 2022

6118.

[german] Zeller, Diana
Medialab – ein dreistufiges Modul zur Entwicklung digitalisierungsbezogener Kompetenzen im Studium des Chemie‐ und Sachunterrichtslehramts
CHEMKON, 29 (S1) :287-292
Juni 2022

6117.

[english] Bohrmann-Linde, Claudia; Zeller, Diana; Meuter, Nico; Tausch, Michael W.
Teaching Photochemistry: Experimental Approaches and Digital Media
ChemPhotoChem, 6 (6) :1-11
Juni 2022

6116.

[german] Kiesling, Elisabeth; Venzlaff, Julian; Bohrmann-Linde, Claudia
BNE im Chemieunterricht – von der Leitlinie BNE NRW zur exemplarischen Unterrichtseinbindung
CHEMKON, 29 (S1) :239-245
Juni 2022

6115.

[german] Zeller, Diana; Meier, Monique
Videos interaktiv erweitern - Forschendes Lernen vielseitig unterstützen
Digital Unterricht Biologie, 4 :10-11
Mai 2022

6114.

[german] Gökkus, Yasemin; Tausch, Michael W.
Explorative Studie zur partizipativen und nutzenorientierten Forschung in der Chemiedidaktik
CHEMKON, 29 (3) :117-124
April 2022

6113.

[german] Banerji, Amitabh; Dörschelln, Jennifer; Schwarz, D.
Organische Leuchtdioden im Chemieunterricht
Chemie in unserer Zeit, 52 (1) :34-41
2022

6112.

Gerlach, Moritz; Glück, Jochen
On characteristics of the range of integral operators
2022

6111.

Petrov, {Pavel S.}; Ehrhardt, Matthias; Trofimov, {M. Yu.}
On the decomposition of the fundamental solution of the {Helmholtz} equation via solutions of iterative parabolic equations
Asymptotic Analysis, 126 (3-4) :215--228
2022
Herausgeber: IOS Press

6110.

Ballaschk, Frederic; Kirsch, Stefan F.
Oxidations with Iodine(V) Compounds – From Stoichiometric Compounds to Catalysts
In Ishihara, Kazuaki and Muñiz, Kilian, Editor, Iodine Catalysis in Organic Synthesis
Seite 299–334
Herausgeber: Wiley
1 Edition
2022
299–334

6109.

Heldmann, F.; Treibert, S.; Ehrhardt, M.; Klamroth, K.
PINN Training using Biobjective Optimization: The Trade-off between Data Loss and Residual Loss
IMACM preprint 22/13
2022

6108.

Jacob, Birgit; Morris, Kirsten
On solvability of dissipative partial differential-algebraic equations
IEEE Control. Syst. Lett., 6 :3188-3193
2022

6107.

Farkas, Bálint; Nagy, Béla; Révész, Szilárd Gy.
On intertwining of maxima of sum of translates functions with nonsingular kernels
Trudy Inst. Mat. Mekh. UrO RAN
2022

6106.

Farkas, Bálint; Jacob, Birgit; Schmitz, Merlin
On exponential splitting methods for semilinear abstract Cauchy problems
2022

6105.

Güttel, Stefan; Schweitzer, Marcel
Randomized sketching for Krylov approximations of large-scale matrix functions
2022

6104.

Klamroth, Kathrin; Stiglmayr, Michael; Sudhoff, Julia
Ordinal Optimization Through Multi-objective Reformulation
math.OC, arXiv:2204.02003
2022
Herausgeber: arXiv

6103.

Kapllani, Lorenc; Teng, Long
Multistep schemes for solving backward stochastic differential equations on {GPU}
JMI, 12 (5)
2022

6102.

Fatoorehchi, Hooman; Ehrhardt, Matthias
Numerical and semi-nume\-rical solutions of a modified Thévenin model for calculating terminal voltage of battery cells
J. Energy Storage, 45 :103746
2022
Herausgeber: Elsevier

6101.

Bartel, Andreas; Günther, Michael
Multirate Schemes -- An Answer of Numerical Analysis to a Demand from Applications
In Michael Günther and Wil Schilders, Editor, Novel Mathematics Inspired by Industrial Challenges
Seite 5--27
Herausgeber: Springer
2022
5--27

6100.

Klamroth, Kathrin; Stiglmayr, Michael; Sudhoff, Julia
Multi-objective Matroid Optimization with Ordinal Weights
Discrete Applied Mathematics
2022

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