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
4877.
Pereselkov, Sergey; Kuz’kin, Venedikt; Ehrhardt, Matthias; Tkachenko, Sergey; Rybyanets, Pavel; Ladykin, Nikolay
Use of interference patterns to control sound field focusing in shallow water
Journal of Marine Science and Engineering, 11 (3) :559
2023
Herausgeber: MDPI4876.
Jendoubi, Oussama
Vergleich der magnetischen Streufeldwerte eines induktiven geladenen Taxis zwischen Simulation und Messung im Rahmen des TALAKO-Projekts
20234875.
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 Press4874.
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 Press4873.
Abdul Halim, Adila; others
Update on the Offline Framework for AugerPrime and production of reference simulation libraries using the VO Auger grid resources
PoS, ICRC2023 :248
20234872.
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/Heidelberg4871.
Dobrick, Alexander; Hölz, Julian
Uniform convergence of solutions to stochastic hybrid models of gene regulatory networks
20234870.
Kapllani, Lorenc; Teng, Long; Rottmann, Matthias
Uncertainty quantification for deep learning-based schemes for solving high-dimensional backward stochastic differential equations
20234869.
Glück, Jochen; Hölz, Julian
Eventual cone invariance revisited
Linear Algebra and its Applications, 675 :274 - 293
20234868.
Kapllani, Lorenc; Teng, Long; Rottmann, Matthias
Uncertainty quantification for deep learning-based schemes for solving high-dimensional backward stochastic differential equations
Submitted to SIAM-ASA J. Uncertain. Quantif.
20234867.
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 Press4866.
Akramov, ME; Yusupov, JR; Ehrhardt, M; Susanto, H; Matrasulov, DU
Transparent boundary conditions for the nonlocal nonlinear Schrödinger equation: A model for reflectionless propagation of PT-symmetric solitons
Physics Letters A :128611
2023
Herausgeber: North-Holland4865.
Dobrick, Alexander; Hölz, Julian; Kunze, Markus
Ultra Feller operators from a functional analytic perspective
20234864.
Lund, Kathryn; Schweitzer, Marcel
The Frechet derivative of the tensor t-function
Calcolo, 60 :35
20234863.
Bolten, Matthias; Donatelli, Marco; Ferrari, Paola; Furci, Isabella
Symbol based convergence analysis in multigrid methods for saddle point problems
Linear Algebra Appl., 671 :67--108
20234862.
Günther, Michael; Sandu, Adrian; Schäfers, Kevin; Zanna, Antonella
Symplectic GARK methods for partitioned Hamiltonian systems
20234861.
Schäfers, Kevin; Günther, Michael; Sandu, Adrian
Symplectic multirate generalized additive Runge-Kutta methods for Hamiltonian systems
Preprint
20234860.
Schäfers, Kevin; Günther, Michael; Sandu, Adrian
Symplectic multirate generalized additive Runge-Kutta methods for Hamiltonian systems
20234859.
Synthesis and evaluation of radioiodinated estrogens for diagnosis and therapy of male urogenital tumours
Organic & Biomolecular Chemistry, 2023 (21) :3090-3095
2023
Herausgeber: RSC
ISSN: 1477-05394858.
Bolten, Matthias; Friedhoff, S.; Hahne, J.
Task graph-based performance analysis of parallel-in-time methods
Parallel Comput., 118 :103050
20234857.
Ehrhardt, Matthias; Kruse, Thomas; Tordeux, Antoine
The Collective Dynamics of a Stochastic Port-Hamiltonian Self-Driven Agent Model in One Dimension
arXiv preprint arXiv:2303.14735
20234856.
Ehrhardt, Matthias; Kruse, Thomas; Tordeux, Antoine
The Collective Dynamics of a Stochastic Port-Hamiltonian Self-Driven Agent Model in One Dimension
arXiv preprint arXiv:2303.14735
20234855.
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
20234854.
Lund, Kathryn; Schweitzer, Marcel
The Frechet derivative of the tensor t-function
Calcolo, 60
20234853.
David, Amelie; Stroka, Steven; Haussmann, Norman; Schmülling, Benedikt; Clemens, Markus
Überprüfung der elektromagnetischen Umweltverträglichkeit bei induktiver Ladung
In Proff, Heike and Clemens, Markus and Marrón, Pedro J. and Schmülling, Benedikt, Editor
Seite 143-180
Herausgeber: Springer Fachmedien Wiesbaden, Wiesbaden
2023
143-180