Related papers: An $\mathcal H_2$-Type Error Bound for Time-Limite…
When solving linear stochastic differential equations numerically, usually a high order spatial discretisation is used. Balanced truncation (BT) and singular perturbation approximation (SPA) are well-known projection techniques in the…
We derive rigorous truncation-error bounds for the spin-boson model and its generalizations to arbitrary quantum systems interacting with bosonic baths. For the numerical simulation of such baths the truncation of both, the number of modes…
In this paper, we explore the role of tensor algebra in balanced truncation (BT) based model reduction/identification for high-dimensional multilinear/linear time invariant systems. In particular, we employ tensor train decomposition (TTD),…
We revisit the method of Carleman linearization for systems of ordinary differential equations with polynomial right-hand sides. This transformation provides an approximate linearization in a higher-dimensional space through the exact…
This paper focuses on providing the high order algorithms for the space-time tempered fractional diffusion-wave equation. The designed schemes are unconditionally stable and have the global truncation error $\mathcal{O}(\tau^2+h^2)$, being…
In this paper, we present a theoretical analysis of the model reduction algorithm for linear switched systems. This algorithm is a reminiscence of the balanced truncation method for linear parameter varying systems. Specifically in this…
This paper studies the data-driven balanced truncation (BT) method for second-order systems based on the measurements in the frequency domain. The basic idea is to approximate Gramians used the numerical quadrature rules, and establish the…
Model order reduction (MOR) techniques are often used to reduce the order of spatially-discretized (stochastic) partial differential equations and hence reduce computational complexity. A particular class of MOR techniques is balancing…
In time-limited model order reduction, a reduced-order approximation of the original high-order model is obtained that accurately approximates the original model within the desired limited time interval. Accuracy outside that time interval…
For a time-limited version of the H$_2$ norm defined over a fixed time interval, we obtain a closed form expression of the gradients. After that, we use the gradients to propose a time-limited model order reduction method. The method…
In this work, we study projection-based model order reduction (MOR) for switched linear systems (SLS) in control form, where the projection matrices are obtained from the solutions of generalized Lyapunov equations (GLEs). We investigate…
The paper proposes a model reduction algorithm for linear hybrid systems, i.e., hybrid systems with externally induced discrete events, with linear continuous subsystems, and linear reset maps. The model reduction algorithm is based on…
An important class of dynamical systems with several practical applications is linear systems with quadratic outputs. These models have the same state equation as standard linear time-invariant systems but differ in their output equations,…
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…
We extend our previous work [F. Henr'iquez and J. S. Hesthaven, arXiv:2403.02847 (2024)] to the linear, second-order wave equation in bounded domains. This technique uses two widely known mathematical tools to construct a fast and efficient…
Linear time-invariant quadratic output (LTIQO) systems generalize linear time-invariant systems to nonlinear regimes. Problems of this class occur in multiple applications naturally, such as port-Hamiltonian systems, optimal control, and…
We present a novel certified model order reduction (MOR) algorithm for switched descriptor systems applicable to large-scale systems. Our algorithm combines the idea of [Hossain \& Trenn, Technical report, 2023] to reformulate the switched…
The theory of nonlinear balanced truncation provides a system-theoretic framework for model reduction that preserves important properties such as stability, controllability, and observability. We present a scalable algorithm for computing…
Along the ideas of Curtain and Glover, we extend the balanced truncation method for infinite-dimensional linear systems to bilinear and stochastic systems. Specifically , we apply Hilbert space techniques used in many-body quantum mechanics…
Efficient high order numerical methods for evolving the solution of an ordinary differential equation are widely used. The popular Runge--Kutta methods, linear multi-step methods, and more broadly general linear methods, all have a global…