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Combined State and Parameter Reduction for Nonlinear Systems with an Application in Neuroscience

Basic data of the doctoral examination procedure

Doctoral examination procedure finished at: Doctoral examination procedure at University of Münster
End date of doctoral examination procedure: 20/06/2016
Name of the doctoral candidate: Himpe, Christian
Doctoral subject: Mathematik
Doctoral degree: Dr. rer. nat.
Awarded by: Department 10 - Mathematics and Computer Science

Description

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.

Projects in which the doctoral examination procedure takes/took place

EXC 1003 Cells in Motion - Imaging to Understand Cellular Behaviour in Organisms (CIM)
Duration: 01/11/2012 - 31/10/2019 | 1st Funding period
Funded by: DFG - Cluster of Excellence
Type of project: Main DFG-project hosted at University of Münster

Publications resulting from doctoral examination procedure

A note on the cross Gramian for non-symmetric systems
Himpe C, Ohlberger M (2016)
In: System Science and Control Engineering, 4(1)
Type of Publication: Research article (journal)
The Versatile Cross Gramian
Himpe C, Ohlberger M (2015)
In: Model Reduction for Parameterized Systems (MoRePaS) III, Trieste, Italy, .
Type of Publication: Abstract in digital collection (conference)
The Empirical Cross Gramian for Parametrized Nonlinear Systems
Himpe C, Ohlberger M (2015)
In: (eds.), . (no publisher available).
Type of Publication: Research article in edited proceedings (conference)
Accelerating the Computation of Empirical Gramians and Related Methods
Himpe C, Ohlberger M (2015)
In: 5th International Workshop on Model Reduction in Reacting Flows, Spreewald, .
Type of Publication: Abstract in digital collection (conference)
Data-driven combined state and parameter reduction for inverse problems
Himpe C, Ohlberger M (2015)
In: Advances in Computational Mathematics, 41(5)
Type of Publication: Research article (journal)
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