Research Foci
- Model Reduction
- Combined State and Parameter Reduction
- Gas Network Simulation
- Dynamic Mode Decomposition
- Knowledge Graphs
Further Affiliation at the University of Münster
Doctoral AbstractThesis
Combined State and Parameter Reduction for Nonlinear Systems with an Application in Neuroscience
- Supervisor
- Professor Dr. Mario Ohlberger
- Doctoral Subject
- Mathematik
- Doctoral Degree
- Dr. rer. nat.
- Awarded by
- Department 10 – Mathematics and Computer Science
This work investigates two complementary methods for combined state and parameter reduction of nonlinear systems. First, a system-theoretic approach using empirical gramians and second, an iterative method utilizing the greedy algorithm. The presented methods are applied in the context of connectivity analysis of neuroimaging data, in which these nonlinear model reduction techniques are demonstrated to accelerate the solution of large-scale inverse problems enabling the data-driven exploration of more complex neuronal networks for example in the human brain.
Project
- Mathematical Research Data Initiative - TA2: Scientific Computing – MaRDI ()
Subproject in DFG-Joint Project Hosted outside the University of Münster: DFG - Nationale Forschungsdateninfrastruktur | Project Number: NFDI 29/1
Articles
- Himpe, Christian, and Grundel, sara. . “System Order Reduction for Gas and Energy Networks.” contribution to the 92nd Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), Aachen doi: 10.1002/pamm.202200201.
- Himpe, C, Grundel, S, and Benner, P. . “Efficient Gas Network Simulations.” in German Success Stories in Industrial Mathematics, Vol. 35 of Mathematics in Industry, edited by HG Bock, KH Küfer, P Maass, A Milde and V Schulz. doi: 10.1007/978-3-030-81455-7_4.
- Benner, P., Burger, M., Göddeke, D., Himpe, C., Hintermüller, M., Heiland, J., Koprucki, T., Ohlberger, M., Rave, S., Reidelbach, M., Saak, J., Schöbel, A., and Tabelow, K. . “Die Mathematische Forschungsdateninitiative in der NFDI: MaRDI (Mathematical Research Data Initiative).” GAMM Rundbrief 1/2022: 40–43.
- Himpe, Christian, Grundel, Sara, and Benner, Peter. . “Next-Gen Gas Network Simulation.” in Progress in Industrial Mathematics at ECMI 2021, Vol. 39 of Mathematics in Industry, edited by Matthias Ehrhardt and Michael Günther. Cham: Springer. doi: 10.1007/978-3-031-11818-0_15.
- Fehr, J, Himpe, C, Rave, S, and Saak, J. . “Sustainable Research Software Hand-Over.” Journal of Open Research Software 9 (1). doi: 10.5334/jors.307/.
- Himpe, C. . “Comparing (Empirical-Gramian-Based) Model Order Reduction Algorithms.” in Model Reduction of Complex Dynamical Systems, Vol. 171 of International Series of Numerical Mathematics, edited by P Benner, T Breiten, H Faßbender, M Hinze, T Stykel and R Zimmermann. doi: 10.1007/978-3-030-72983-7_7.
- Himpe, C, Grundel, S, and Benner, P. . “Model Order Reduction for Gas and Energy Networks.” Journal of Mathematics in Industry 11: 13.. doi: 10.1186/s13362-021-00109-4.
- Clees, T, Baldin, A, Benner, P, Grundel, S, Himpe, C, Klaassen, B, Küsters, F, Marheineke, N, Nikitina, L, Nikitin, I, Pade, J, Stahl, N, Strohm, C, Tischendorf, C, and Wirsen, A. . “MathEnergy – Mathematical Key Technologies for Evolving Energy Grids.” in Mathematical Modeling, Simulation and Optimization for Power Engineering and Management, Vol. 34 of Mathematics in Industry, edited by S Göttlich, M Herty and A Milde. doi: 10.1007/978-3-030-62732-4_11.
- Benner, P, and Himpe, C. . “Cross-Gramian-Based Dominant Subspaces.” Advances in Computational Mathematics 45 (5): 2533–2553. doi: 10.1007/s10444-019-09724-7.
- Grundel, S, Himpe, C, and Saak, J. . “On Empirical System Gramians.” in Vol. 19 of Proceedings in Applied Mathematics and Mechanics (PAMM) doi: 10.1002/pamm.201900006.
- Himpe, C, Leibner, T, and Rave, S. . “Hierarchical Approximate Proper Orthogonal Decomposition.” SIAM Journal on Scientific Computing 40 (5): A3267–A3292.
- Benner, P, Himpe, C, and Mitchell, T. . “On Reduced Input-Output Dynamic Mode Decomposition.” Advances in Computational Mathematics 44 (6): 1751–1768. doi: 10.1007/s10444-018-9592-x.
- Benner, P, Grundel, S, Himpe, C, Huck, C, Streubel, T, and Tischendorf, C. . “Gas Network Benchmark Models.” in Applications of Differential-Algebraic Equations: Examples and Benchmarks, Differential-Algebraic Equations Forum, edited by S Campbell, A Ilchmann, V Mehrmann and T Reis. doi: 10.1007/11221_2018_5.
- Himpe, C. . “emgr - The Empirical Gramian Framework.” Algorithms 11 (7): 91.. doi: 10.3390/a11070091.
- Benner, P, Grundel, S, and Himpe, C. . “Parametric Model Order Reduction for Gas Flow Models.” in Vol. MoRePaS 4 of ScienceOpen Posters ScienceOpen. doi: 10.14293/P2199-8442.1.SOP-MATH.EJOCET.v1.
- Himpe, C, Leibner, T, and Rave, S. . “HAPOD - Fast, Simple and Reliable Distributed POD Computation.” in Vol. 55 of ARGESIM Report doi: 10.11128/arep.55.a55283.
- Baur, U, Benner, P, Haasdonk, B, Himpe, C, Martini, I, and Ohlberger, M. . “Comparison of methods for parametric model order reduction of instationary problems.” in Model Reduction and Approximation: Theory and Algorithms., Vol. 15 of CS, edited by P Benner, A Cohen, M Ohlberger and K Willcox. Philadelphia, PA: SIAM Publications. doi: 10.1137/1.9781611974829.ch9.
- Himpe, C, and Ohlberger, M. . “Cross-Gramian-Based Model Reduction: A Comparison.” in Model Reduction of Parametrized Systems, Vol. 17 of MS&A (Modeling, Simulation and Applications), edited by P Benner, M Ohlberger, A Patera, G Rozza and K Urban. Cham: Springer International Publishing. doi: 10.1007/978-3-319-58786-8_17.
- Himpe, C, Leibner, T, Rave, S, and Saak, J. . “Fast Low-Rank Empirical Cross Gramians.” PAMM 17 (1): 841–842. doi: 10.1002/pamm.201710388.
- Himpe, C, and Ohlberger, M. . “A note on the cross Gramian for non-symmetric systems.” System Science and Control Engineering 4 (1): 199–208. doi: 10.1080/21642583.2016.1215273.
- Fehr, J, Heiland, J, Himpe, C, and Saak, J. . “Best Practices for Replicability, Reproducibility and Reusability of Computer-Based Experiments Exemplified by Model Reduction.” AIMS Mathematics 1 (3): 261--281. doi: 10.3934/Math.2016.3.261.
- Himpe, C, and Ohlberger, M. . “The Versatile Cross Gramian.” in Vol. Morepas 3 of ScienceOpen Posters scienceopen. doi: 10.14293/P2199-8442.1.SOP-MATH.PSAHPZ.v1.
- Himpe, C, and Ohlberger, M. . “The Empirical Cross Gramian for Parametrized Nonlinear Systems.” in Vol. 48(1) of IFAC-PapersOnLine doi: 10.1016/j.ifacol.2015.05.163.
- Himpe, C, and Ohlberger, M. . “Accelerating the Computation of Empirical Gramians and Related Methods.” contribution to the 5th International Workshop on Model Reduction in Reacting Flows, Spreewald doi: 10.5281/zenodo.46643.
- Himpe, C, and Ohlberger, M. . “Data-driven combined state and parameter reduction for inverse problems.” Advances in Computational Mathematics 41 (5): 1343–1364. doi: 10.1007/s10444-015-9420-5.
- Himpe, C, and Ohlberger, M. . “Model Reduction for Complex Hyperbolic Networks.” contribution to the 13th European Control Conference (ECC), June 24-27, 2014, Strasbourg, France Wiley-IEEE Press. doi: 10.1109/ECC.2014.6862188.
- Himpe, C, and Ohlberger, M. . “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.
- Himpe, C, and Ohlberger, M. . “Combined State and Parameter Reduction.” in Vol. 14 of Proceedings in Applied Mathematics and Mechanics (PAMM) doi: 10.1002/pamm.201410393.
- Himpe, C, and Ohlberger, M. . “A Unified Software Framework for Empirical Gramians.” Journal of Mathematics 2013 (2013): 1–6. doi: 10.1155/2013/365909.