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
4837.
Hendricks, C; Ehrhardt, M; Günther, M
High order tensor product interpolation in the Combination Technique
preprint, 14 :254836.
Ehrhardt, Matthias; Brunner, H
Mathematical Modelling of Monkeypox Epidemics4835.
Hendricks, Christian; Ehrhardt, Matthias; Günther, Michael
Hybrid finite difference/pseudospectral methods for stochastic volatility models
19th European Conference on Mathematics for Industry, Seite 388- 2024
4834.
Sprachsensibler Chemieunterricht digital umgesetzt - Ein Seminarexkurs im Rahmen des Praxissemesters
20244833.
Ambartsumyan, I; Khattatov, E; Yotov, I; Zunino, P; Arnold, Anton; Ehrhardt, Matthias; Ashyralyev, Allaberen; Csom{\'o}s, Petra; Farag{\'o}, Istv{\'a}n; Fekete, Imre; others
Invited Papers4832.
Ambartsumyan, I; Khattatov, E; Yotov, I; Zunino, P; Arnold, Anton; Ehrhardt, Matthias; Ashyralyev, Allaberen; Csomós, Petra; Faragó, István; Fekete, Imre; others
Invited Papers4831.
Günther, Michael; Kossaczk{\`y}, Igor
Lab Exercises for Numerical Analysis and Simulation I: ODEs4830.
Ehrhardt, Matthias; Günther, Michael; Brunner, H; Dalhoff, A
Mathematical Modelling of Dengue Fever Epidemics4829.
Ehrhardt, Matthias; Günther, Michael; Brunner, H; Dalhoff, A
Mathematical Modelling of Dengue Fever Epidemics4828.
Ehrhardt, Matthias; Brunner, H
Mathematical Modelling of Monkeypox Epidemics4827.
Ehrhardt, Matthias; Günther, Michael; Brunner, H
Mathematical Study of Grossman's model of investment in health capital4826.
Maten, E Jan W; Ehrhardt, Matthias
MS40: Computational methods for finance and energy markets
19th European Conference on Mathematics for Industry, Seite 3774825.
Ehrhardt, Matthias; Günther, Michael; Brunner, H
Mathematical Study of Grossman's model of investment in health capital4824.
Ehrhardt, M; Günther, M; Bartel, PD Dr A
Mathematische Modellierung in Anwendungen4823.
Silva, JP; Maten, J; Günther, M; Ehrhardt, M
Model Order Reduction Techniques for Basket Option Pricing4822.
Silva, JP; Maten, J; Günther, M; Ehrhardt, M
Model Order Reduction Techniques for Basket Option Pricing4821.
Ehrhardt, Matthias; Günther, Michael
Modelling Stochastic Correlations in Finance4820.
Ehrhardt, Matthias; Günther, Michael
Modelling Stochastic Correlations in Finance4819.
Ehrhardt, Matthias; Günther, Michael; Jacob, Birgit; Bartel, PD Dr Andreas; Maten, Jan
Modelling, Analysis and Simulation with Port-Hamiltonian Systems4818.
Ehrhardt, Matthias; Günther, Michael; Jacob, Birgit; Bartel, PD Dr Andreas; Maten, Jan
Modelling, Analysis and Simulation with Port-Hamiltonian Systems4817.
Hendricks, Christian; Ehrhardt, Matthias; Günther, Michael
Hybrid finite difference/pseudospectral methods for stochastic volatility models
19th European Conference on Mathematics for Industry, Seite 388- 2024
4816.
Ackermann, Julia; Ehrhardt, Matthias; Kruse, Thomas; Tordeux, Antoine
Stabilisation of stochastic single-file dynamics using port-Hamiltonian systems
arXiv preprint arXiv:2401.17954
20244815.
Bartel, Andreas; Diab, Malak; Frommer, Andreas; Günther, Michael; Marheineke, Nicole
Splitting Techniques for DAEs with port-Hamiltonian Applications
Preprint
20244814.
Günther, M.; Jacob, Birgit; Totzeck, Claudia
Data-driven adjoint-based calibration of port-Hamiltonian systems in time domain
Math. Control Signals Syst.
20244813.
Klass, Friedemann; Gabbana, Alessandro; Bartel, Andreas
Characteristic boundary condition for thermal lattice Boltzmann methods
Computers & Mathematics with Applications, 157 :195–208
2024
Herausgeber: Pergamon