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



2023

4655.

Kossaczká, Tatiana; Ehrhardt, Matthias; Günther, Michael
Deep finite difference method for solving Asian option pricing problems
Preprint IMACM
2023

4654.

Kapllani, Lorenc; Teng, Long
Deep Learning algorithms for solving high-dimensional nonlinear Backward Stochastic Differential Equations
Discrete Contin. Dyn. Syst. - B
2023
ISSN: 1531-3492

4653.

Kapllani, Lorenc; Teng, Long
Deep Learning algorithms for solving high-dimensional nonlinear backward stochastic differential equations
Discrete Contin. Dyn. Syst. - B
2023

4652.

Ackermann, Julia; Jentzen, Arnulf; Kruse, Thomas; Kuckuck, Benno; Padgett, Joshua Lee
Deep neural networks with ReLU, leaky ReLU, and softplus activation provably overcome the curse of dimensionality for Kolmogorov partial differential equations with Lipschitz nonlinearities in the $L^p$-sense
2023

4651.

Ackermann, Julia; Jentzen, Arnulf; Kruse, Thomas; Kuckuck, Benno; Padgett, Joshua Lee
Deep neural networks with ReLU, leaky ReLU, and softplus activation provably overcome the curse of dimensionality for Kolmogorov partial differential equations with Lipschitz nonlinearities in the Lp-sense
Preprint
2023

4650.

Abdul Halim, Adila; others
Deep-Learning-Based Cosmic-Ray Mass Reconstruction Using the Water-Cherenkov and Scintillation Detectors of AugerPrime
PoS, ICRC2023 :371
2023

4649.

Kowol, Philipp; Bargmann, Swantje; Görrn, Patrick; Wilmers, Jana
Delamination Behavior of Highly Stretchable Soft Islands Multi-Layer Materials
Applied Mechanics, 4 (2) :514--527
2023
ISSN: 2673-3161

4648.

Klamroth, Kathrin; Lang, Bruno; Stiglmayr, Michael
Efficient Dominance Filtering for Unions and Minkowski Sums of Non-Dominated Sets
Computers and Operations Research
2023
Herausgeber: Elsevier {BV}

4647.

Abdul Halim, Adila; others
Constraints on UHECR characteristics from cosmogenic neutrino limits with the measurements of the Pierre Auger Observatory
PoS, ICRC2023 :1520
2023

4646.

Poggi, Aurora; Di Persio, Luca; Ehrhardt, Matthias
Electricity Price Forecasting via Statistical and Deep Learning Approaches: The German Case
AppliedMath, 3 (2) :316--342
2023
Herausgeber: Multidisciplinary Digital Publishing Institute

4645.

Poggi, Aurora; Di Persio, Luca; Ehrhardt, Matthias
Electricity Price Forecasting via Statistical and Deep Learning Approaches: The German Case
AppliedMath, 3 (2) :316--342
2023
Herausgeber: Multidisciplinary Digital Publishing Institute

4644.

Glück, Jochen; Hölz, Julian
Eventual cone invariance revisited
Linear Algebra and its Applications, 675 :274 - 293
2023

4643.

Janssen, Nils; Fetzer, Jana R; Grewing, Jannis; Burgmann, Sebastian; Janoske, Uwe
Experimental investigation of particle--droplet--substrate interaction
Experiments in Fluids, 64 (3) :44
2023
Herausgeber: Springer Berlin Heidelberg Berlin/Heidelberg

4642.

Ehrhardt, Matthias; Pereselkov, Sergey; Kuz’kin, Venedikt; Kaznacheev, Ilya; Rybyanets, Pavel
Experimental observation and theoretical analysis of the low-frequency source interferogram and hologram in shallow water
Journal of Sound and Vibration, 544 :117388
März 2023
Herausgeber: Academic Press

4641.

Ehrhardt, Matthias; Pereselkov, Sergey; Kuz’kin, Venedikt; Kaznacheev, Ilya; Rybyanets, Pavel
Experimental observation and theoretical analysis of the low-frequency source interferogram and hologram in shallow water
Journal of Sound and Vibration, 544 :117388
2023
Herausgeber: Academic Press

4640.

Ehrhardt, Matthias; Pereselkov, Sergey; Kuz’kin, Venedikt; Kaznacheev, Ilya; Rybyanets, Pavel
Experimental observation and theoretical analysis of the low-frequency source interferogram and hologram in shallow water
Journal of Sound and Vibration, 544 :117388
2023
Herausgeber: Academic Press

4639.

Kääpä, Alex; Kampert, Karl-Heinz; Becker Tjus, Julia
Flux predictions in the transition region incorporating the effects from propagation of cosmic rays in the Galactic magnetic field
EPJ Web Conf., 283 :03006
2023

4638.

Petrov, Pavel; Matskovskiy, Andrey; Zakharenko, Alena; Zavorokhin, German; Dosso, Stan
Generalized Pekeris-Buldyrev waveguide and its properties
submitted to J. Acoust. Soc. Am.
Juni 2023

4637.

Abel, Ulrich; Acu, Ana Maria; Heilmann, Margareta; Raşa, Ioan
Genuine Bernstein–Durrmeyer type operators preserving 1 and $x^j$
Annals of Functional Analysis, 15 (1)
Oktober 2023
Herausgeber: Springer Science and Business Media LLC
ISSN: 2008-8752

4636.

Haussmann, Norman; Stroka, Steven; Schmuelling, Benedikt; Clemens, Markus
GPU-accelerated body-internal electric field exposure simulation using low-frequency magnetic field sampling points
COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, 42 (5) :982-992
01 2023
Herausgeber: Emerald Publishing Limited
ISSN: 0332-1649

4635.

Stroka, S.; Haussmann, N.; Zang, M.; Schmuelling, B.; Clemens, M.
GPU-Based Near Real-Time Estimation of the Human Body Penetrating Low-Frequency Magnetic Fields Using Free-Space Field Measurements
IEEE Transactions on Magnetics, 59 (5) :1-4
2023

4634.

[german] Gökkus, Yasemin; Kremer, Richard; Zeller, Diana; Bohrmann-Linde, Claudia
H5P angereicherte Videos für den Chemieunterricht und die Lehrkräfteausbildung
In Bohrmann-Linde, C.; Gökkuş, Y.; Kremer, R.; Zeller, D., Editor, Band Netzwerk Digitalisierter Chemieunterricht. Sammelband NeDiChe-Treff 2021
Seite 9-18
Herausgeber: Chemiedidaktik. Bergische Universität Wuppertal
2023
9-18

4633.

Abdul Halim, Adila; others
Constraints on upward-going air showers using the Pierre Auger Observatory data
PoS, ICRC2023 :1099
2023

4632.

Yue, Baobiao; others
Constraints on BSM particles from the absence of upward-going air showers in the Pierre Auger Observatory
PoS, ICRC2023 :1095
2023

4631.


Improved Common $t\bar{t}$ Monte-Carlo Settings for ATLAS and CMS
CERN, Geneva
2023

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