Forschungsschwerpunkte
- Modellreduktion
- Kombinierte Zustands- und Parameterraumreduktion
- Simulation von Gasnetzwerken
- Dynamic Mode Decomposition
- Knowledge Graphen
Weitere Zugehörigkeit an der Universität Münster
Promotion
Combined State and Parameter Reduction for Nonlinear Systems with an Application in Neuroscience
- Betreuer
- Professor Dr. Mario Ohlberger
- Promotionsfach
- Mathematik
- Abschlussgrad
- Dr. rer. nat.
- Verleihender Fachbereich
- Fachbereich 10 – Mathematik und Informatik
Diese Arbeit untersucht zwei komplementäre Methoden für die kombinierte Zustandsund Parameterreduktion von nichtlinearen Systemen. Einerseits wird ein systemtheoretischer Ansatz untersucht, der empirische Gram-Matrizen benutzt, andererseits eine iterative Methode, die den Greedy-Algorithmus verwendet. Die vorgestellten Methoden werden auf die Konnektivitätsanalyse aus neurobildgebenden Verfahren angewandt, für welche gezeigt wird, dass diese nichtlineare Modellreduktion die Lösung des inversen Problems beschleunigt. was eine datengetriebene Erforschung von komplexeren neuronalen Netzwerken erlaubt, zum Beispiel für das menschliche Gehirn.Projekt
- MaRDI – Mathematische Forschungsdateninitiative - TA2: Scientific Computing ( – )
Teilprojekt in DFG-Verbund koordiniert außerhalb der Universität Münster: DFG - Nationale Forschungsdateninfrastruktur | Förderkennzeichen: NFDI 29 /1
- MaRDI – Mathematische Forschungsdateninitiative - TA2: Scientific Computing ( – )
Publikationen
- . . ‘System Order Reduction for Gas and Energy Networks.’ Contributed to the 92nd Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), Aachen. doi: 10.1002/pamm.202200201.
- . . ‘Efficient Gas Network Simulations.’ In German Success Stories in Industrial Mathematics, edited by , 17–22. doi: 10.1007/978-3-030-81455-7_4.
- „Die Mathematische Forschungsdateninitiative in der NFDI: MaRDI (Mathematical Research Data Initiative).“ GAMM Rundbrief 1/2022: 40–43. .
- . . ‘Next-Gen Gas Network Simulation.’ In Progress in Industrial Mathematics at ECMI 2021, edited by , 107–113. Heidelberg: Springer. doi: 10.1007/978-3-031-11818-0_15.
- . . ‘Sustainable Research Software Hand-Over.’ Journal of Open Research Software 9, Nr. 1. doi: 10.5334/jors.307/.
- . . ‘Comparing (Empirical-Gramian-Based) Model Order Reduction Algorithms.’ In Model Reduction of Complex Dynamical Systems, edited by , 141–164. doi: 10.1007/978-3-030-72983-7_7.
- . . ‘Model Order Reduction for Gas and Energy Networks.’ Journal of Mathematics in Industry 11: 13. doi: 10.1186/s13362-021-00109-4.
- . . ‘MathEnergy – Mathematical Key Technologies for Evolving Energy Grids.’ In Mathematical Modeling, Simulation and Optimization for Power Engineering and Management, edited by , 233–262. doi: 10.1007/978-3-030-62732-4_11.
- . . ‘Cross-Gramian-Based Dominant Subspaces.’ Advances in Computational Mathematics 45, Nr. 5: 2533–2553. doi: 10.1007/s10444-019-09724-7.
- . . ‘On Empirical System Gramians.’ Contributed to the 90th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), Wien, Österrreich. doi: 10.1002/pamm.201900006.
- . . ‘Hierarchical Approximate Proper Orthogonal Decomposition.’ SIAM Journal on Scientific Computing 40, Nr. 5: A3267–A3292.
- . . ‘On Reduced Input-Output Dynamic Mode Decomposition.’ Advances in Computational Mathematics 44, Nr. 6: 1751–1768. doi: 10.1007/s10444-018-9592-x.
- . . ‘Gas Network Benchmark Models.’ In Applications of Differential-Algebraic Equations: Examples and Benchmarks, edited by , 171–197. doi: 10.1007/11221_2018_5.
- . . ‘emgr - The Empirical Gramian Framework.’ Algorithms 11, Nr. 7: 91. doi: 10.3390/a11070091.
- . „Parametric Model Order Reduction for Gas Flow Models.“ contributed to the MoRePaS 4 - Model Reduction for Parameterized Systems, Nantes, Frankreich, . doi: 10.14293/P2199-8442.1.SOP-MATH.EJOCET.v1.
- . „HAPOD - Fast, Simple and Reliable Distributed POD Computation.“ contributed to the MATHMOD 2018- 9th Vienna International Conference on Mathematical Modelling, Vienna, . doi: 10.11128/arep.55.a55283.
- . . ‘Comparison of methods for parametric model order reduction of instationary problems.’ In Model Reduction and Approximation: Theory and Algorithms., edited by , 377–408. 1. Aufl. Philadelphia: SIAM Publications. doi: 10.1137/1.9781611974829.ch9.
- . . ‘Cross-Gramian-Based Model Reduction: A Comparison.’ In Model Reduction of Parametrized Systems, edited by , 271–283. Basel : Springer International Publishing. doi: 10.1007/978-3-319-58786-8_17.
- . . ‘Fast Low-Rank Empirical Cross Gramians.’ PAMM 17, Nr. 1: 841–842. doi: 10.1002/pamm.201710388.
- . . ‘Best Practices for Replicability, Reproducibility and Reusability of Computer-Based Experiments Exemplified by Model Reduction.’ AIMS Mathematics 1, Nr. 3: 261--281. doi: 10.3934/Math.2016.3.261.
- . . ‘A note on the cross Gramian for non-symmetric systems.’ System Science and Control Engineering 4, Nr. 1: 199–208. doi: 10.1080/21642583.2016.1215273.
- . „The Versatile Cross Gramian.“ contributed to the Model Reduction for Parameterized Systems (MoRePaS) III, Trieste, Italy, . doi: 10.14293/P2199-8442.1.SOP-MATH.PSAHPZ.v1.
- . . ‘The Empirical Cross Gramian for Parametrized Nonlinear Systems.’ Contributed to the MATHMOD 2015 - 8th Vienna International Conference on Mathematical Modelling, Vienna. doi: 10.1016/j.ifacol.2015.05.163.
- . „Accelerating the Computation of Empirical Gramians and Related Methods.“ contributed to the 5th International Workshop on Model Reduction in Reacting Flows, Spreewald, . doi: 10.5281/zenodo.46643.
- . . ‘Data-driven combined state and parameter reduction for inverse problems.’ Advances in Computational Mathematics 41, Nr. 5: 1343–1364. doi: 10.1007/s10444-015-9420-5.
- . . ‘Model Reduction for Complex Hyperbolic Networks.’ Contributed to the 13th European Control Conference (ECC), June 24-27, 2014, Strasbourg, France. doi: 10.1109/ECC.2014.6862188.
- . . ‘Cross-Gramian Based Combined State and Parameter Reduction for Large-Scale Control Systems.’ Mathematical Problems in Engineering 2014: 1–13. doi: 10.1155/2014/843869.
- . . ‘Combined State and Parameter Reduction.’ Contributed to the 85th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), Erlangen. doi: 10.1002/pamm.201410393.
- . . ‘A Unified Software Framework for Empirical Gramians.’ Journal of Mathematics 2013, Nr. 2013: 1–6. doi: 10.1155/2013/365909.
Dr. Christian Himpe
Professur für Angewandte Mathematik, insbesondere Numerik (Prof. Ohlberger)
Weitere Publikationen