Dr. Martin Redmann
Computational Methods in Systems and Control Theory
Max Planck Institute for Dynamics of Complex Technical Systems
Max Planck Institute for Dynamics of Complex Technical Systems
Main Focus
- Numerical Approximations to Rough (P)DEs
- Lévy Processes
- Stochastic Ordinary Differential Equations
- Stochastic Evolution Equations
- Model Reduction for Stochastic Systems
- Balanced Truncation for Linear Controlled Stochastic Differential Equations with Lévy Noise
- Singular Perturbation Approximation for Linear Controlled Stochastic Differential Equations with Lévy Noise
- Error Bound and Stability Analysis for Model Order Reduction Methods for Stochastic Systems
- Galerkin Schemes for Controlled Stochastic Partial Differential Equations with Lévy Noise
Curriculum Vitae
- since 07/2016 Weierstraß Institute for Applied Analysis and Stochastics in Berlin, Postdoctoral researcher in mathematics
- 06/2012 – 06/2016 Max Planck Institute for Dynamics of Complex Technical Systems in Magdeburg, Ph.D. student in mathematics, research interest: Model Order Reduction Techniques Applied to Evolution Equations with Lévy Noise
- 10/2009 – 04/2012 Martin-Luther-Universität Halle-Wittenberg, Studies in Mathematics (major) and Economics (minor) with main focus on stochastics, Degree: Master of Science, Masters’ thesis: Zur Stochastischen Analysis Hilbertraum-wertiger Lévy-Prozesse (The Stochastic Analysis of Hilbert Space-valued Lévy Processes)
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10/2006 – 09/2009 Martin-Luther-Universität Halle-Wittenberg, Studies in Mathematics (major) and Economics (minor), Degree: Bachelor of Science, Bachelor thesis: Ein zeitdiskretes fraktales Filterproblem (A Time Discrete Fractional Filtering Problem)
Preprints
- P. Benner, P. Goyal, and M. Redmann, Truncated Gramians for Bilinear Systems and their Advantages in Model Order Reduction, Submitted June 2016
- P. Benner and M. Redmann, Singular Perturbation Approximation for Linear Systems with Lévy Noise, MPIMD/15-22, Max Planck Institute Magdeburg, 2015
- P. Benner and M. Redmann, An ℋ₂-Type Error Bound for Balancing-Related Model Order Reduction of Linear Systems with Lévy Noise, MPIMD/15-20, Max Planck Institute Magdeburg, 2015
Publications
- P. Benner and M. Redmann, Approximation and Model Order Reduction for Second Order Systems with Lévy-Noise, AIMS Proceedings, 2015
- P. Benner and M. Redmann, Model Reduction for Stochastic Systems, Stochastic Partial Differential Equations: Analysis and Computations, 2015
- P. Benner, T. Damm, M. Redmann, and Y. R. Rodriguez Cruz, Positive Operators and Stable Truncation, Linear Algebra and its Applications, 2014
- P. Benner and M. Redmann, Reachability and Observability Concepts for Stochastic Systems, Proc. Appl. Math. Mech., 2013
Talks
- Model Order Reduction for Linear Controlled SDEs with Lévy Noise; Joint DMV and GAMM Annual Meeting; Braunschweig; March 2016
- An Overview of Balancing Related Model Order Reduction for Systems with Lévy Noise; 12th German Probability and Statistics Days; Bochum; March 2016
- Model Order Reduction for Linear Controlled SDEs with Lévy Noise; Numerical Analysis Seminar at the University of Bath (invited by Dr. Melina Freitag); Bath; December 2015
- Balancing Related Model Order Reduction Applied to Linear Controlled SPDEs with Lévy Noise; Workshop on 'Stochastic Analysis 2015: Halle-Jena-Leipzig'; Halle; October 2015
- Singular Perturbation Approximation Applied to SPDEs; ENUMATH Conference; Ankara; September 2015
- Singular Perturbation Approximation Applied to SPDEs; Winter School on Stochastic Analysis of Spatially Extended Models; Darmstadt; March 2015
- Balancing Related Model Order Reduction Applied to SPDEs; Seminar talk at the University of Warwick (Prof. Andrew Stuart’s group); Coventry; February 2015
- Stochastic PDEs - Approximation and MOR; 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications; Madrid; July 25, 2014
- Model Order Reduction for Stochastic Systems; Seminar talk at the University of Kaiserslautern (Prof. Tobias Damm’s group); Kaiserslautern; March 2014
- Model Order Reduction for Linear Stochastic Differential Equations with Lévy Noise; 11th German Probability and Statistics Days; Ulm; March 4, 2014
- Projektionsmethoden zur Lösung stochastischer Evolutionsgleichungen; 9th Workshop for Doctoral Students of the Probability and Statistics Group; Göttingen, Germany; August 2, 2013
- Balanced Truncation for Stochastic Linear Systems with Lévy Noise; 84th GAMM Annual Meeting; Novi Sad, Serbia; March 21, 2013
- Balanced Truncation for Stochastic Differential Equations with Lévy Noise; Elgersburg Workshop, February 11 - 14, 2013; Elgersburg, Germany; February 13, 2013