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



2024

4880.

Levron, Yoash; Valadez, Alan; Weiss, George
Testing the Local Stability of a Multi-Machine Power System with Constant Power Loads
2024

4879.

Ehrhardt, Matthias; Kruse, Thomas; Tordeux, Antoine
The collective dynamics of a stochastic port-Hamiltonian self-driven agent model in one dimension
ESAIM: Mathematical Modelling and Numerical Analysis, 58 (2) :515–544
2024
Publisher: EDP Sciences

4878.

Rohde, Martin; Burgmann, Sebastian; Janoske, Uwe
The impact of a two-dimensional vibration excitation on the critical incident flow velocity of a sessile droplet
International Journal of Multiphase Flow, 171 :104663
2024
Publisher: Pergamon

4877.

Reiter, Kendra; Schmidt, Marie; Stiglmayr, Michael
The Line-Based Dial-a-Ride Problem
In Bouman, Paul C. and Kontogiannis, Spyros C., Editor, 24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024)Volume123fromOpen Access Series in Informatics (OASIcs), Page 14:1—14:20
24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024). Open Access Series in Informatics (OASIcs)
In Bouman, Paul C. and Kontogiannis, Spyros C., Editor
Publisher: Schloss Dagstuhl — Leibniz-Zentrum für Informatik, Dagstuhl, Germany
2024

4876.

Ehrhardt, Matthias; Zheng, Chunxiong
für Angewandte Analysis und Stochastik
2024

4875.

[german] Zeller, Diana; Bohrmann-Linde, Claudia; Mack, Nils; Diekmann, Charlotte; Schrader, Claudia
Virtual Reality für den Chemieunterricht
Nachrichten aus der Chemie, 72 (6) :15-22
2024

4874.

Kapllani, Lorenc; Teng, Long; Rottmann, Matthias
Uncertainty quantification for deep learning-based schemes for solving high-dimensional backward stochastic differential equations
To appear in International Journal of Uncertainty Quantification
2024
Publisher: Begell

4873.

Hendricks, Christian; Ehrhardt, Matthias; Günther, Michael
Hybrid finite difference/pseudospectral methods for stochastic volatility models
19th European Conference on Mathematics for Industry, Page 388

4872.

Ehrhardt, Matthias; Zheng, Chunxiong
für Angewandte Analysis und Stochastik

4871.

Ehrhardt, Matthias
Positive Schemes for Air Pollution Problems, Optimal Location of Industrial Enterprises and Optimization of their Emissions

4870.

Günther, Michael; Wandelt, Dipl Math Mich{\`e}le
Numerical Analysis and Simulation I: ODEs

4869.

Ehrhardt, Matthias; Günther, Michael
Numerical Evaluation of Complex Logarithms in the Cox-Ingersoll-Ross Model

4868.

Ehrhardt, Matthias; Günther, Michael
Numerical Pricing of Game (Israeli) Options

4867.

Ehrhardt, Matthias; Günther, Michael
Numerical Pricing of Game (Israeli) Options

4866.

Ehrhardt, Matthias; Farkas, Bálint; Günther, Michael; Jacob, Birgit; Bartel, PD Dr Andreas
Operator Splitting and Multirate Schemes

4865.

Ehrhardt, Matthias; Farkas, B{\'a}lint; Günther, Michael; Jacob, Birgit; Bartel, PD Dr Andreas
Operator Splitting and Multirate Schemes

4864.

Calvo-Garrido, MC; Ehrhardt, M; V{\'a}zquez, C
PDE modeling and numerical methods for swing option pricing in electricity markets
19th European Conference on Mathematics for Industry, Page 390

4863.

Calvo-Garrido, MC; Ehrhardt, M; Vázquez, C
PDE modeling and numerical methods for swing option pricing in electricity markets
19th European Conference on Mathematics for Industry, Page 390

4862.

Acu, A.M.; Heilmann, Margareta; Raşa, I.
Voronovskaja type results for the Aldaz-Kounchev-Render versions of generalized Baskakov Operators
submitted

4861.

Maten, E Jan W; Ehrhardt, Matthias
MS40: Computational methods for finance and energy markets
19th European Conference on Mathematics for Industry, Page 377

4860.

Ehrhardt, Matthias
Positive Schemes for Air Pollution Problems, Optimal Location of Industrial Enterprises and Optimization of their Emissions

4859.

Carmen Calvo-Garrido, Mar{\i}a; Ehrhardt, Matthias; V{\'a}zquez, Carlos
Pricing swing options in electricity markets with two stochastic factors: PIDE modeling and numerical solution
3rd International Conference on Computational Finance (ICCF2019), Page 89

4858.

Carmen Calvo-Garrido, Mar{\i}a; Ehrhardt, Matthias; Vázquez, Carlos
Pricing swing options in electricity markets with two stochastic factors: PIDE modeling and numerical solution
3rd International Conference on Computational Finance (ICCF2019), Page 89

4857.

Putek, PA; Ter Maten, EJW; Günther, M
Reliability-based Low Torque Ripple Design of Permanent Magnet Machine

4856.

Günther, M; Ehrhardt, M; Knechtli, F; Shcherbakov, D; Striebel, M; Wandelt, M
Symmetric \& Volume Preserving Projection Schemes

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