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We propose an experimental study of adaptive time-stepping methods for efficient modeling of the aggregation-fragmentation kinetics. Precise modeling of this phenomena usually requires utilization of the large systems of nonlinear ordinary…

Numerical Analysis · Mathematics 2025-01-20 Sergey A. Matveev , Viktor Zhilin , Alexander P. Smirnov

This paper proposes a data-driven model reduction approach on the basis of noisy data. Firstly, the concept of data reduction is introduced. In particular, we show that the set of reduced-order models obtained by applying a Petrov-Galerkin…

Optimization and Control · Mathematics 2022-02-01 Azka Muji Burohman , Bart Besselink , Jacquelien M. A. Scherpen , M. Kanat Camlibel

We consider an optimization problem related to semi-active damping of vibrating systems. The main problem is to determine the best damping matrix able to minimize influence of the input on the output of the system. We use a minimization…

Dynamical Systems · Mathematics 2017-07-07 Zoran Tomljanović , Christopher Beattie , Serkan Gugercin

A common approach in model reduction is balanced truncation, which is based on gramian matrices classifiying certain attributes of states or parameters of a given dynamic system. Initially restricted to linear systems, the empirical…

Optimization and Control · Mathematics 2016-08-22 Christian Himpe , Mario Ohlberger

We consider the numerical solution of large-scale symmetric differential matrix Riccati equations. Under certain hypotheses on the data, reduced order methods have recently arisen as a promising class of solution strategies, by forming…

Numerical Analysis · Mathematics 2020-01-14 Gerhard Kirsten , Valeria Simoncini

We develop time integration methods in low-rank representation that can adaptively adjust approximation ranks to achieve a prescribed accuracy, while ensuring that these ranks remain proportional to the corresponding best approximation…

Numerical Analysis · Mathematics 2025-07-22 Markus Bachmayr , Matthieu Dolbeault , Polina Sachsenmaier

Considering the use of dynamical systems in practical applications, often only limited regions in the time or frequency domain are of interest. Therefor, it usually pays off to compute local approximations of the used dynamical systems in…

Optimization and Control · Mathematics 2021-05-17 Peter Benner , Steffen W. R. Werner

A new method for data-driven interpolatory model reduction is presented in this paper. Using the so-called data informativity perspective, we define a framework that enables the computation of moments at given (possibly complex)…

Systems and Control · Electrical Eng. & Systems 2022-04-29 Azka Muji Burohman , Bart Besselink , Jacquelien M. A. Scherpen , M. Kanat Camlibel

This paper deals with the balanced truncation model reduction of discrete-time, linear time-varying, heterogeneous subsystems interconnected over finite arbitrary directed graphs. The information transfer between the subsystems is subject…

Optimization and Control · Mathematics 2017-08-15 Dany Abou Jaoude , Mazen Farhood

Interpolation-based methods are well-established and effective approaches for the efficient generation of accurate reduced-order surrogate models. Common challenges for such methods are the automatic selection of good or even optimal…

Numerical Analysis · Mathematics 2024-07-23 Quirin Aumann , Steffen W. R. Werner

The aim in model order reduction is to approximate an input-output map described by a large-scale dynamical system with a low-dimensional and cheaper-to-evaluate reduced order model. While high fidelity can be achieved by a variety of…

Dynamical Systems · Mathematics 2023-01-04 Björn Liljegren-Sailer

In this paper, balancing based model order reduction (MOR) for large-scale linear discrete-time time-invariant systems in prescribed finite time intervals is studied. The first main topic is the development of error bounds regarding the…

Numerical Analysis · Mathematics 2019-02-06 Igor Pontes Duff , Patrick Kürschner

Recent years have witnessed a wave of research activities in systems science toward the study of population systems. The driving force behind this shift was geared by numerous emerging and ever-changing technologies in life and physical…

Optimization and Control · Mathematics 2019-08-16 Jr-Shin Li , Wei Zhang , Lin Tie

In computational and applied statistics, it is of great interest to get fast and accurate calculation for the distributions of the quadratic forms of Gaussian random variables. This paper presents a novel approximation strategy that…

Methodology · Statistics 2023-12-29 Hong Zhang , Judong Shen , Zheyang Wu

In this paper we study the problem of model reduction by moment matching for stochastic systems. We characterize the mathematical object which generalizes the notion of moment to stochastic differential equations and we find a class of…

Systems and Control · Electrical Eng. & Systems 2021-05-06 Giordano Scarciotti , Andrew R. Teel

A wide range of implicit time integration methods, including multi-step, implicit Runge-Kutta, and Galerkin finite-time element schemes, is evaluated in the context of chaotic dynamical systems. The schemes are applied to solve the Lorenz…

Computational Physics · Physics 2024-01-02 Viktoriya Morozova , James G. Coder , Kevin Holst

We propose an efficient algorithm for the approximation of fractional integrals by using Runge--Kutta based convolution quadrature. The algorithm is based on a novel integral representation of the convolution weights and a special…

Numerical Analysis · Mathematics 2019-07-29 Lehel Banjai , María López-Fernández

The numerical integration of an analytical function $f(x)$ using a finite set of equidistant points can be performed by quadrature formulas like the Newton-Cotes. Unlike Gaussian quadrature formulas however, higher-order Newton-Cotes…

Numerical Analysis · Mathematics 2021-08-24 Irfan Muhammad

Balanced truncation is a well-established model order reduction method which has been applied to a variety of problems. Recently, a connection between linear Gaussian Bayesian inference problems and the system-theoretic concept of balanced…

Numerical Analysis · Mathematics 2024-01-04 Josie König , Melina A. Freitag

Port-Hamiltonian systems provide an energy-based modeling paradigm for dynamical input-state-output systems. At their core, they fulfill an energy balance relating stored, dissipated and supplied energy. To accurately resolve this energy…

Numerical Analysis · Mathematics 2024-12-17 Andreas Bartel , Manuel Schaller