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Research Areas
- Model Reduction
- Combined State and Parameter Reduction
- Gas Network Simulation
- Dynamic Mode Decomposition
- Knowledge Graphs
Doctoral Thesis
Combined State and Parameter Reduction for Nonlinear Systems with an Application in Neuroscience
- Supervisor
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.
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Project
- MaRDI - Mathematical Research Data Initiative - TA2: Scientific Computing ( – )
Subproject in DFG-joint project hosted outside WWU: DFG - National Research Data Infrastructure | Project Number: NFDI 29 /1
- MaRDI - Mathematical Research Data Initiative - TA2: Scientific Computing ( – )
Publications
- . . ‘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.
- . . ‘Sustainable Research Software Hand-Over.’ Journal of Open Research Software 9, No. 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, No. 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, No. 5: A3267–A3292.
- . . ‘On Reduced Input-Output Dynamic Mode Decomposition.’ Advances in Computational Mathematics 44, No. 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, No. 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. 1st Ed. Philadelphia, PA: 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. Cham: Springer International Publishing. doi: 10.1007/978-3-319-58786-8_17.
- . . ‘Fast Low-Rank Empirical Cross Gramians.’ PAMM 17, No. 1: 841–842. doi: 10.1002/pamm.201710388.
- . . ‘A note on the cross Gramian for non-symmetric systems.’ System Science and Control Engineering 4, No. 1: 199–208. doi: 10.1080/21642583.2016.1215273.
- . . ‘Best Practices for Replicability, Reproducibility and Reusability of Computer-Based Experiments Exemplified by Model Reduction.’ AIMS Mathematics 1, No. 3: 261--281. doi: 10.3934/Math.2016.3.261.
- . ‘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, No. 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, No. 2013: 1–6. doi: 10.1155/2013/365909.
Dr. Christian Himpe
Professorship of Applied Mathematics, especially Numerics (Prof. Ohlberger)
