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
- 1990
312.
Jensen, Per; Bunker, Philip R.; Karpfen, Alfred; Kofranek, Manfred; Lischka, Hans
An ab initio calculation of the intramolecular stretching spectra for the HF dimer and its D-substituted isotopic species
The Journal of Chemical Physics, 93 (9) :6266-6280
1990311.
Jensen, Per; Buenker, Robert J.; Hirsch, Gerhard; Rai, Sachchida N.
An ab initio calculation of the rotational-vibrational energies in the electronic ground state of NH\(_{2}\)
Molecular Physics, 70 (3) :443-454
1990310.
Jensen, Per; Bunker, Philip R.; Karpfen, Alfred; Kofranek, Manfred; Lischka, Hans
An ab initio calculation of the intramolecular stretching spectra for the HF dimer and its D-substituted isotopic species
The Journal of Chemical Physics, 93 (9) :6266-6280
1990309.
Jensen, Per; Bunker, Philip R.; Karpfen, Alfred; Kofranek, Manfred; Lischka, Hans
An ab initio calculation of the intramolecular stretching spectra for the HF dimer and its D-substituted isotopic species
The Journal of Chemical Physics, 93 (9) :6266-6280
1990308.
Bunker, Philip R.; Jensen, Per; Karpfen, Alfred; Kofranek, Manfred; Lischka, Hans
An ab initio calculation of the stretching energies for the HF dimer
The Journal of Chemical Physics, 92 (12) :7432-7440
1990307.
Bunker, Philip R.; Jensen, Per; Wright, J. S.; Hamilton, I. P.
Ab initio rotation-vibration energies and intensities for the H2F+ molecule
Journal of Molecular Spectroscopy, 144 (2) :310-322
1990306.
Bunker, Philip R.; Jensen, Per; Wright, J. S.; Hamilton, I. P.
Ab initio rotation-vibration energies and intensities for the H\(_{2}\)F\(^{+}\) molecule
Journal of Molecular Spectroscopy, 144 (2) :310-322
1990305.
Bunker, Philip R.; Jensen, Per; Wright, J. S.; Hamilton, I. P.
Ab initio rotation-vibration energies and intensities for the H\(_{2}\)F\(^{+}\) molecule
Journal of Molecular Spectroscopy, 144 (2) :310-322
1990304.
Tausch, Michael W.; Kühn, S.
''Chemische Gleichgewichte - Elektrochemie'' - Diskette mit Programmen zu STOFF UND FORMEL II, Lehrbuch für die S II (Grundkurse)
Herausgeber: C. C. Buchner, Bamberg
1990303.
Jensen, Per; Buenker, Robert J.; Hirsch, Gerhard; Rai, Sachchida N.
An ab initio calculation of the rotational-vibrational energies in the electronic ground state of NH2
Molecular Physics, 70 (3) :443-454
1990302.
Bunker, Philip R.; Jensen, Per; Karpfen, Alfred; Kofranek, Manfred; Lischka, Hans
An ab initio calculation of the stretching energies for the HF dimer
The Journal of Chemical Physics, 92 (12) :7432-7440
1990301.
Jensen, Per; Buenker, Robert J.; Hirsch, Gerhard; Rai, Sachchida N.
An ab initio calculation of the rotational-vibrational energies in the electronic ground state of NH\(_{2}\)
Molecular Physics, 70 (3) :443-454
1990300.
Tausch, Michael W.; Deissenberger, H.; Fischer, W.; Hoffmann, W.; Jakob, O.; Riedl, A.; Schallies, M.; Wachtendonk, M.
STOFF UND FORMEL II, Lehrbuch für die S II (Grundkurse), 325 Seiten
Herausgeber: C. C. Buchner, Bamberg
1990299.
Bunker, Philip R.; Jensen, Per; Karpfen, Alfred; Kofranek, Manfred; Lischka, Hans
An ab initio calculation of the stretching energies for the HF dimer
The Journal of Chemical Physics, 92 (12) :7432-7440
1990298.
Heilmann, Margareta; Müller, Manfred
Direct and converse results on simultaneous approximation by the method of Bernstein-Durrmeyer operators
Algorithms for approximation II, Proc. 2nd Int. Conf., Shrivenham/UK 1988, Seite 107-116
1990297.
Fink, Ewald H.; Kruse, H.; Setzer, Klaus-Dieter; Ramsay, D. A.; Vervloet, M.
High resolution Fourier-transform spectra of the a\(^{1}\)\(\Delta\)\(_{g}\) → X\(^{3}\)\(\Sigma\)\(_{g}\)\(^{-}\), b\(^{1}\)\(\Sigma\)\(_{g}\)\(^{+}\) → X\(^{3}\)\(\Sigma\)\(_{g}\)\(^{-}\) and X\(^{1}\)\(\Sigma\)\(_{g}\)\(^{+}\) → a\(^{1}\)\(\Delta\)\(_{g}\) systems of O\(_{2}\), SO, S\(_{2}\) and isoe
Acta Physica Hungarica, 67 (1-2) :67-72
1990296.
Fink, Ewald H.; Kruse, H.; Setzer, Klaus-Dieter; Ramsay, D. A.; Vervloet, M.
High resolution Fourier-transform spectra of the a\(^{1}\)\(\Delta\)\(_{g}\) → X\(^{3}\)\(\Sigma\)\(_{g}\)\(^{-}\), b\(^{1}\)\(\Sigma\)\(_{g}\)\(^{+}\) → X\(^{3}\)\(\Sigma\)\(_{g}\)\(^{-}\) and X\(^{1}\)\(\Sigma\)\(_{g}\)\(^{+}\) → a\(^{1}\)\(\Delta\)\(_{g}\) systems of O\(_{2}\), SO, S\(_{2}\) and isoe
Acta Physica Hungarica, 67 (1-2) :67-72
1990295.
Fink, Ewald H.; Kruse, H.; Setzer, Klaus-Dieter; Ramsay, D. A.; Vervloet, M.
High resolution Fourier-transform spectra of the a1Δg → X3Σg-, b1Σg+ → X3Σg- and X1Σg+ → a1Δg systems of O2, SO, S2 and isoe
Acta Physica Hungarica, 67 (1-2) :67-72
1990294.
Fink, Ewald H.; Setzer, Klaus-Dieter; Ramsay, D. A.; Vervloet, M.; Brown, John M.
High-resolution study of the A 1-X 0\(^{+}\) emission system of bismuth hydride
Journal of Molecular Spectroscopy, 142 (1) :108-116
1990293.
Fink, Ewald H.; Setzer, Klaus-Dieter; Ramsay, D. A.; Vervloet, M.; Brown, John M.
High-resolution study of the A 1-X 0\(^{+}\) emission system of bismuth hydride
Journal of Molecular Spectroscopy, 142 (1) :108-116
1990292.
Fink, Ewald H.; Setzer, Klaus-Dieter; Ramsay, D. A.; Vervloet, M.; Brown, John M.
High-resolution study of the A 1-X 0+ emission system of bismuth hydride
Journal of Molecular Spectroscopy, 142 (1) :108-116
1990291.
Tausch, Michael W.; Deissenberger, H.; Fischer, W.; Hoffmann, W.; Jakob, O.; Riedl, A.; Schallies, M.; Wachtendonk, M.
Lehrerband mit didaktischen Hinweisen und Lösungen der Aufgaben zu STOFF UND FORMEL II, Lehrbuch für die S II (Grundkurse)
Herausgeber: C. C. Buchner, Bamberg
1990290.
Ehrhardt, M
Technische Universität Berlin Wintersemester 06/07 Fakultät II--Institut für Mathematik
SIAM J. Appl. Math, 50 :1442--1456
1990289.
Ehrhardt, M
Technische Universität Berlin Wintersemester 06/07 Fakultät II--Institut für Mathematik
SIAM J. Appl. Math, 50 :1442--1456
1990- 1989
288.
[german] Tausch, Michael W.; Wöhrle, D.
Photokatalyse
Praxis der Naturwissenschaften (Chemie), 38 :37
1989