Martin Redmann
YOU?
Author Swipe
View article: (Empirical) Gramian-based dimension reduction for stochastic differential equations driven by fractional Brownian motion
(Empirical) Gramian-based dimension reduction for stochastic differential equations driven by fractional Brownian motion Open
In this paper we investigate large-scale linear systems driven by a fractional Brownian motion (fBm) with Hurst parameter $H\in [1/2, 1)$ . We interpret these equations either in the sense of Young ( $H>1/2$ ) or Stratonovich ( $H=1/2$ ). …
View article: Exact dimension reduction for rough differential equations
Exact dimension reduction for rough differential equations Open
In this paper, practically computable low-order approximations of potentially high-dimensional differential equations driven by geometric rough paths are proposed and investigated. In particular, equations are studied that cover the linear…
View article: Dimension reduction for path signatures
Dimension reduction for path signatures Open
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 collections of iterated integrals along paths, is discussed and th…
View article: Dimension reduction for large-scale stochastic systems with non-zero initial states and controlled diffusion
Dimension reduction for large-scale stochastic systems with non-zero initial states and controlled diffusion Open
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 transforms the original setting into a stochastic system with z…
View article: Learning Stochastic Reduced Models from Data: A Nonintrusive Approach
Learning Stochastic Reduced Models from Data: A Nonintrusive Approach Open
A nonintrusive model order reduction method for bilinear stochastic differential equations with additive noise is proposed. A reduced order model (ROM) is designed in order to approximate the statistical properties of high-dimensional syst…
View article: Model reduction for stochastic systems with nonlinear drift
Model reduction for stochastic systems with nonlinear drift Open
In this paper, we study dimension reduction techniques for large-scale controlled stochastic differential equations (SDEs). The drift of the considered SDEs contains a polynomial term satisfying a one-sided growth condition. Such nonlinear…
View article: Complexity reduction of large-scale stochastic systems using linear quadratic Gaussian balancing
Complexity reduction of large-scale stochastic systems using linear quadratic Gaussian balancing Open
In this paper, we consider a model reduction technique for stabilizable and detectable stochastic systems. It is based on a pair of Gramians that we analyze in terms of well-posedness. Subsequently, dominant subspaces of the stochastic sys…
View article: Model order reduction methods applied to neural network training
Model order reduction methods applied to neural network training Open
Neural networks have emerged as powerful and versatile tools in the field of deep learning. As the complexity of the task increases, so do size and architectural complexity of the network, causing compression techniques to become a focus o…
View article: (Empirical) Gramian-based dimension reduction for stochastic differential equations driven by fractional Brownian motion
(Empirical) Gramian-based dimension reduction for stochastic differential equations driven by fractional Brownian motion Open
In this paper, we investigate large-scale linear systems driven by a fractional Brownian motion (fBm) with Hurst parameter $H\in [1/2, 1)$. We interpret these equations either in the sense of Young ($H>1/2$) or Stratonovich ($H=1/2$). Espe…
View article: Exact dimension reduction for rough differential equations
Exact dimension reduction for rough differential equations Open
In this paper, practically computable low-order approximations of potentially high-dimensional differential equations driven by geometric rough paths are proposed and investigated. In particular, equations are studied that cover the linear…
View article: Sampling‐based model order reduction for stochastic differential equations driven by fractional Brownian motion
Sampling‐based model order reduction for stochastic differential equations driven by fractional Brownian motion Open
In this paper, we study large‐scale linear fractional stochastic systems representing, e.g., spatially discretized stochastic partial differential equations (SPDEs) driven by fractional Brownian motion (fBm) with Hurst parameter H > ½. Suc…
View article: Complexity reduction of large-scale stochastic systems using linear quadratic Gaussian balancing
Complexity reduction of large-scale stochastic systems using linear quadratic Gaussian balancing Open
In this paper, we consider a model reduction technique for stabilizable and detectable stochastic systems. It is based on a pair of Gramians that we analyze in terms of well-posedness. Subsequently, dominant subspaces of the stochastic sys…
View article: Model reduction for stochastic systems with nonlinear drift
Model reduction for stochastic systems with nonlinear drift Open
In this paper, we study dimension reduction techniques for large-scale controlled stochastic differential equations (SDEs). The drift of the considered SDEs contains a polynomial term satisfying a one-sided growth condition. Such nonlinear…
View article: Runge-Kutta Methods for Rough Differential Equations
Runge-Kutta Methods for Rough Differential Equations Open
We study Runge-Kutta methods for rough differential equations which can be used to calculate solutions to stochastic differential equations driven by processes that are rougher than a Brownian motion.We use a Taylor series representation (…
View article: Gramian-based model reduction for unstable stochastic systems
Gramian-based model reduction for unstable stochastic systems Open
This paper considers large-scale linear stochastic systems representing, e.g., spatially discretized stochastic partial differential equations. Since asymptotic stability can often not be ensured in such a stochastic setting (e.g., due to …
View article: Solving high-dimensional optimal stopping problems using optimization based model order reduction
Solving high-dimensional optimal stopping problems using optimization based model order reduction Open
Solving optimal stopping problems by backward induction in high dimensions is often very complex since the computation of conditional expectations is required. Typically, such computations are based on regression, a method that suffers fro…
View article: Full state approximation by Galerkin projection reduced order models for stochastic and bilinear systems
Full state approximation by Galerkin projection reduced order models for stochastic and bilinear systems Open
In this paper, the problem of full state approximation by model reduction is studied for stochastic and bilinear systems. Our proposed approach relies on identifying the dominant subspaces based on the reachability Gramian of a system. Onc…
View article: Gramian-based model reduction for unstable stochastic systems
Gramian-based model reduction for unstable stochastic systems Open
This paper considers large-scale linear stochastic systems representing, e.g., spatially discretized stochastic partial differential equations. Since asymptotic stability can often not be ensured in such a stochastic setting (e.g. due to l…
View article: Model order reduction for bilinear systems with non-zero initial states -- different approaches with error bounds
Model order reduction for bilinear systems with non-zero initial states -- different approaches with error bounds Open
In this paper, we consider model order reduction for bilinear systems with non-zero initial conditions. We discuss choices of Gramians for both the homogeneous and the inhomogeneous parts of the system individually and prove how these Gram…
View article: Full state approximation by Galerkin projection reduced order models for\n stochastic and bilinear systems
Full state approximation by Galerkin projection reduced order models for\n stochastic and bilinear systems Open
In this paper, the problem of full state approximation by model reduction is\nstudied for stochastic and bilinear systems. Our proposed approach relies on\nidentifying the dominant subspaces based on the reachability Gramian of a\nsystem. …
View article: Low-Dimensional Approximations of High-Dimensional Asset Price Models
Low-Dimensional Approximations of High-Dimensional Asset Price Models Open
We consider high-dimensional asset price models that are reduced in their dimension in order to reduce the complexity of the problem or the effect of the curse of dimensionality in the context of option pricing. We apply model order reduct…
View article: Bilinear Systems---A New Link to $\mathcal H_2$-norms, Relations to Stochastic Systems, and Further Properties
Bilinear Systems---A New Link to $\mathcal H_2$-norms, Relations to Stochastic Systems, and Further Properties Open
In this paper, we prove several new results that give new insights into bilinear systems. We discuss conditions for asymptotic stability using probabilistic arguments. Moreover, we provide a global characterization of reachability in bilin…
View article: Dynamic programming for optimal stopping via pseudo-regression
Dynamic programming for optimal stopping via pseudo-regression Open
We introduce new variants of classical regression-based algorithms for optimal stopping problems based on computation of regression coefficients by Monte Carlo approximation of the corresponding L2 inner products instead of the least-squar…
View article: Runge--Kutta methods for rough differential equations
Runge--Kutta methods for rough differential equations Open
We study Runge-Kutta methods for rough differential equations which can be used to calculate solutions to stochastic differential equations driven by processes that are rougher than a Brownian motion. We use a Taylor series representation …
View article: Error bounds for model reduction of feedback-controlled linear stochastic dynamics on Hilbert spaces
Error bounds for model reduction of feedback-controlled linear stochastic dynamics on Hilbert spaces Open
We analyze structure-preserving model order reduction methods for Ornstein-Uhlenbeck processes and linear S(P)DEs with multiplicative noise based on balanced truncation. For the first time, we include in this study the analysis of non-zero…
View article: Feedback control theory & Model order reduction for stochastic equations
Feedback control theory & Model order reduction for stochastic equations Open
We analyze structure-preserving model order reduction methods for Ornstein-Uhlenbeck processes and linear SPDEs with multiplicative noise based on balanced truncation with non-zero initial data. We then marry these model order reduction me…