Martin Redmann - Personal Homepage
- Address:
Martin Luther University of Halle Wittenberg, Institute of Mathematics,
Theodor-Lieser-Str. 5, 06120 Halle (Saale)
- Office: Theodor-Lieser-Str. 5, Georg-Cantor-Haus, room E.15.0,
- Phone: +49-345-55-24672,
- Fax: +49-345-55-27003,
- E-Mail: martin.redmann@mathematik.uni-halle.de
I worked within the research group Stochastic
Algorithms and Nonparametric Statistics at the Weierstraß Institute for
Applied Analysis and Stochastics. I was a member of the DFG Research Unit - Rough Paths, Stochastic Partial Differential Equations and Related Topics and I was a postdoctoral researcher within the subproject
Numerical Analysis of Rough PDEs. I was also a part of the research group Quantitative analysis of stochastic and rough systems.
From August 2018 to January 2019 I worked as an Interim Professor at the University of Southern Denmark.
Since January 2020 I am the Head of the Chair for Applied Stochastics at the Martin Luther University of Halle-Wittenberg.
Research Interests
- 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
Short CV
- since 01/2020 Martin Luther University of Halle-Wittenberg, Assistant Professor (W1 with Tenure Track to W2) for Applied Stochastics (Head of the Chair)
- 08/2018 − 01/2019 University of Southern Denmark (Odense): Department of Mathematics and Computer Science, Interim Professor
- 07/2016 − 12/2019 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, Ph.D. thesis: Model Order Reduction Techniques Applied to Evolution Equations with Lévy Noise
- 10/2009 − 04/2012 Martin Luther University of 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)
- 10/2006 − 09/2009 Martin Luther University of 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)
Current Research Grants
- since 10/2022 DFG Individual Grant: Head of the project "Low-order approximations for large-scale problems arising in the context of high-dimensional PDEs and spatially discretized SPDEs" (GZ: RE 4767/3; Project-Nr.: 499366908), Funds: PhD position for 3 years and related funds (approximately 213 000 EUR)
Preprints
Publications
- M. Redmann, Model reduction for stochastic systems with nonlinear drift, Journal of Mathematical Analysis and Applications, 2024
- T. Damm, M. Redmann, Complexity reduction of large-scale stochastic systems using linear quadratic Gaussian balancing, Journal of the Franklin Institute, 2023
- M. A. Freitag, J. M. Nicolaus, M. Redmann, Model order reduction methods applied to neural network training, Proc. Appl. Math. Mech., 2023
- N. Jamshidi, M. Redmann, Sampling-based model order reduction for stochastic differential equations driven by fractional Brownian motion, Proc. Appl. Math. Mech., 2023
- M. Redmann, Solving high-dimensional optimal stopping problems using optimization based model order reduction, Applied Mathematical Finance, 2023
- M. Redmann, S. Riedel, Runge-Kutta methods for rough differential equations, Journal of Stochastic Analysis, 2022
- M. Redmann, N. Jamshidi, Gramian-based model reduction for unstable stochastic systems, Mathematics of Control, Signals, and Systems, 2022
- S. Becker, C. Hartmann, M. Redmann, L. Richter, Error bounds for model reduction of feedback-controlled linear stochastic dynamics on Hilbert spaces, Stochastic Processes and their Applications, 2022
- M. Redmann, I. Pontes Duff, Model order reduction for bilinear systems with non-zero initial states -- different approaches with error bounds, International Journal of Control, 2022
- M. Redmann, I. Pontes Duff, Full state approximation by Galerkin projection reduced order models for stochastic and bilinear systems, Applied Mathematics and Computation, 2022
- M. Redmann, Bilinear systems -- A new link to H2-norms, relations to stochastic systems and further properties, SIAM Journal on Control and Optimization, 2021
- M. Redmann, M. Freitag, Optimization based model order reduction for stochastic systems, Applied Mathematics and Computation, 2021
- M. Redmann, C. Bayer, P. Goyal, Low-dimensional approximations of high-dimensional asset price models, SIAM Journal on Financial Mathematics, 2021
- C. Bayer, D. Belomestny, M. Redmann, S. Riedel, J. Schoenmakers, Solving linear parabolic rough partial differential equations, Journal of Mathematical Analysis and Applications, 2020
- M. Redmann, A new type of singular perturbation approximation for stochastic bilinear systems, Mathematics of Control, Signals, and Systems, 2020
- C. Bayer, M. Redmann, J. Schoenmakers, Dynamic programming for optimal stopping via pseudo-regression, Quantitative Finance, 2020
- M. Redmann, An L2T-error bound for time-limited balanced truncation, Systems and Control Letters, 2020
- P. Goyal, M. Redmann, Time-Limited H2-Optimal Model Order Reduction, Applied Mathematics and Computation, 2019
- M. Redmann, Energy estimates and model order reduction for stochastic bilinear systems, International Journal of Control, 2018
- M. Freitag and M. Redmann, Balanced Model Order Reduction for Linear Random Dynamical Systems Driven by Lévy Noise, Journal of Computational Dynamics, 2018
- P. Kürschner, M. Redmann, An Output Error Bound for Time-Limited Balanced Truncation, Systems and Control Letters, 2018
- M. Redmann, Type II balanced truncation for deterministic bilinear control systems, SIAM Journal on Control and Optimization, 2018
- M. Redmann, Type II singular perturbation approximation for linear systems with Lévy Noise, SIAM Journal on Control and Optimization, 2018
- P. Benner and M. Redmann, Singular Perturbation Approximation for Linear Systems with Lévy Noise, Stochastics and Dynamics, 2017
- P. Benner and M. Redmann, An H2-Type Error Bound for Balancing-Related Model Order Reduction of Linear Systems with Lévy Noise, Systems and Control Letters, 2017
- P. Benner, P. Goyal, and M. Redmann, Truncated Gramians for Bilinear Systems and their Advantages in Model Order Reduction, Model Reduction of Parametrized Systems, MS&A - Modeling, Simulation and Applications, Springer International Publishing, 2017
- 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
Further Publications
Talks
- Exact dimension reduction for rough differential equations; Workshop "Mathematics, Data Science, and Education" (invited talk); Hagen; March 2024
- Model reduction for stochastic systems with nonlinear drift; ENUMATH 2023(invited talk); Lisbon; September 2023
- Solving stochastic and rough differential equations efficiently; Saale-Elster-Colloquium(invited talk); Halle-Jena-Leipzig; May 2023
- Working on mathematical modelling for problems in automated driving and medical imaging; 2nd SFB 1294 (Data Assimilation) Data Think Tank(invited event); Potsdam; March 2023
- Optimization-Based Model Order Reduction with Applications in Finance; SIAM CSE(invited talk); Amsterdam; February/March 2023
- Numerical approximations of rough (partial) differential equations; Oberseminar Stochastik(invited talk); Jena; November 2022
- Optimization based model order reduction for stochastic systems; Workshop on "Model Reduction and Surrogate Modeling (MORE)"; Berlin; September 2022
- Complexity reduction for high-dimensional SDEs - an introduction with applications; Workshop "Stochastic and Rough Analysis" (invited talk); Berlin; August 2022
- Solving high-dimensional optimal stopping problems using model order reduction; Seminar "Modern Methods in Applied Stochastics and Nonparametric Statistics" at the Weierstrass Institute (invited talk); Berlin; May 2022
- Low-dimensional approximations of high-dimensional asset price models; 13th International Workshop on Stochastic Models and Control; Lübeck-Travemünde (Germany); March 2022
- Error analysis of system-theoretic model reduction for bilinear systems; SIAM Conference on Control and Its Applications (invited talk); Spokane, Washington (U.S.); July 2021
- Stochastic Differential Equations - An Introduction with Applications; Mathematical Colloquium at the Middle East Technical University (invited talk); Ankara; April 2021
- Bilinear systems -- An output bound and its consequences; 91st GAMM Annual Meeting; Kassel; March 2021
- Runge-Kutta methods for rough differential equations; 14th Oxford-Berlin Young Researchers Meeting on Applied Stochastic Analysis (invited talk); Oxford; February 2021
- Stochastic Differential Equations - Applications and Efficient Solutions; Mathematical Colloquium at the University of Cottbus (invited talk); Cottbus; March 2020
- Energy estimates and model order reduction for bilinear systems with Lévy noise; European Numerical Mathematics and
Advanced Applications Conference (invited talk); Egmond aan Zee; October 2019
- Model Reduction for Stochastic Bilinear Systems; International Congress on Industrial and Applied Mathematics; Valencia; July 2019
- Numerical approximations for RDEs and SDEs; Seminar talk at the University of Dresden (invited talk); Dresden; April 2019
- Numerical approximations for RDEs and SDEs; Seminar talk at the University of Freiberg (invited talk); Freiberg (Germany); April 2019
- Energy estimates and model order reduction for stochastic bilinear systems; 12th International Workshop on Stochastic Models and Control; Cottbus; March 2019
- Numerical approximations for RDEs and SDEs; Seminar talk at the University of Halle (invited talk); Halle; December 2018
- Numerical approximations for RDEs and SDEs; Seminar talk at the University of Potsdam (invited talk); Potsdam; December 2018
- Numerical approximations for rough and stochastic differential equations; Seminar talk at the University of Aachen (invited talk); Aachen; October 2018
- Numerical approximations of parabolic rough PDEs; Harmonic Analysis for Stochastic PDEs; Delft; July 2018
- Solving parabolic rough partial differential equations using regression; 13th International Conference in Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing (invited talk); Rennes; July 2018
- Solving stochastic (partial) differential equations; Seminar talk at the University of Greifswald (invited talk); Greifswald (Germany); April 2018
- Numerical approximations of parabolic rough PDEs; 13th German Probability and Statistics Days; Freiburg; March 2018
- Beyond the theory of ordinary differential equations; Seminar talk at the Department of Mathematics and Computer Science (invited talk); Odense (Denmark); February 2018
- Type II singular perturbation approximation for linear systems with Lévy noise; EPSRC Durham Symposium on
Model Order Reduction (invited talk); Durham (UK); August 2017
- A regression method to solve parabolic rough PDEs; Ninth Workshop on
Random Dynamical Systems (invited talk); Bielefeld; June 2017
- A regression method to solve parabolic rough PDEs; 7th Annual ERC Berlin-Oxford Young Researchers Meeting on Applied Stochastic Analysis (invited talk); Berlin; May 2017
- Model reduction for stochastic differential equations; Stochastic Analysis Seminar in Oxford (invited by Prof. Terry Lyons); Oxford; October 2016
- Low Order Approximations to Linear SPDEs with Lévy Noise; 5th Annual ERC Berlin-Oxford Young Researchers Meeting on Applied Stochastic Analysis (invited talk); Berlin; August 2016
- Alternative Approaches to "Standard" Balanced Truncation for Linear Systems Driven by Lévy Noise; CSC/NDS Workshop on Computational Methods for High-Dimensional Problems; Schloss Ringberg (Tegernsee); May 2016
- 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 (SPA) angewendet auf SPDEs; Stochastic Analysis Seminar at the University of Halle (invited by Prof. Wilfried Grecksch); Halle, Germany; May 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 (invited by Prof. Andrew Stuart); 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 (invited by Prof. Tobias Damm); Kaiserslautern; March 2014
- Model Order Reduction for Linear Stochastic Differential Equations with Lévy Noise; 11th German Probability and Statistics Days; Ulm; March 4, 2014
- Modellreduktion für lineare stochastische Evolutionsgleichungen mit Lévy-Rauschen; Stochastic Analysis Seminar at the University of Halle (invited by Prof. Wilfried Grecksch); Halle, Germany; November 28, 2013
- 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