14 citations · 21 across the 21 of their papers we have counts for
27 papers
Tree-based solution representations for quadratic bilinear systems and their consequences in model order reduction
Martin Redmann
We investigate quadratic bilinear systems by developing novel tree-based representations of their solutions. The proposed framework decomposes the solution into a sequence of coupl…
Signature-Based Universal Bilinear Approximations for Nonlinear Systems and Model Order Reduction
Martin Redmann, Justus Werner
This paper deals with non-Lipschitz nonlinear systems. Such systems can be approximated by a linear map of so-called signatures, which play a crucial role in the theory of rough pa…
Model reduction for fully nonlinear stochastic systems
Martin Redmann
This paper presents a novel model order reduction framework tailored for fully nonlinear stochastic dynamics without lifting them to quadratic systems and without using linearizati…
Dimension reduction for path signatures
Christian Bayer, Martin Redmann
This paper focuses on the mathematical framework for reducing the complexity of models using path signatures. The structure of these signatures, which can be interpreted as collect…
Dimension reduction for large-scale stochastic systems with non-zero initial states and controlled diffusion
Martin Redmann
In this paper, we establish new strategies to reduce the dimension of large-scale controlled stochastic differential equations with non-zero initial states. The first approach tran…
(Empirical) Gramian-based dimension reduction for stochastic differential equations driven by fractional Brownian motion
Nahid Jamshidi, Martin Redmann
In this paper, we investigate large-scale linear systems driven by a fractional Brownian motion (fBm) with Hurst parameter . We interpret these equations either in t…