Related papers: Stability preservation in Galerkin-type projection…
We investigate linear dynamical systems consisting of ordinary differential equations with high dimensionality. Model order reduction yields alternative systems of much lower dimensions. However, a reduced system may be unstable, although…
Mathematical modeling often yields linear dynamical systems in science and engineering. We change physical parameters of the system into random variables to perform an uncertainty quantification. The stochastic Galerkin method yields a…
In uncertainty quantification, critical parameters of mathematical models are substituted by random variables. We consider dynamical systems composed of ordinary differential equations. The unknown solution is expanded into an orthogonal…
We examine nonlinear dynamical systems of ordinary differential equations or differential algebraic equations. In an uncertainty quantification, physical parameters are replaced by random variables. The inner variables as well as a quantity…
Projection-based nonlinear model order reduction methods can be used to reduce simulation times for the solution of many PDE-constrained problems. It has been observed in literature that such nonlinear reduced-order models (ROMs) based on…
We propose a projection-based model order reduction method for the solution of parameter-dependent dynamical systems. The proposed method relies on the construction of time-dependent reduced spaces generated from evaluations of the solution…
This work proposes a method for model reduction of finite-volume models that guarantees the resulting reduced-order model is conservative, thereby preserving the structure intrinsic to finite-volume discretizations. The proposed…
Two comprehensive approaches are considered for constructing projection-based reduced-order computational models for linear dynamical systems. The first one reduces the governing equations written in the descriptor form, using a Galerkin or…
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. Once…
We propose a probabilistic way for reducing the cost of classical projection-based model order reduction methods for parameter-dependent linear equations. A reduced order model is here approximated from its random sketch, which is a set of…
This work presents a novel stabilization strategy for the Galerkin formulation of the incompressible Navier-Stokes equations, developed to achieve high accuracy while ensuring convergence and compatibility with high-order elements on…
This paper presents a novel model order reduction framework tailored for fully nonlinear stochastic dynamics without lifting them to quadratic systems and without using linearization techniques. By directly leveraging structural properties…
Invariance and stability are essential notions in dynamical systems study, and thus it is of great interest to learn a dynamics model with a stable invariant set. However, existing methods can only handle the stability of an equilibrium. In…
In the Reduced Basis approximation of Stokes and Navier-Stokes problems, the Galerkin projection on the reduced spaces does not necessarily preserved the inf-sup stability even if the snapshots were generated through a stable full order…
Hyperexponential stability is investigated for dynamical systems with the use of both, explicit and implicit, Lyapunov function methods. A nonlinear hyperexponential control is designed for stabilizing linear systems. The tuning procedure…
In this work a stabilised and reduced Galerkin projection of the incompressible unsteady Navier-Stokes equations for moderate Reynolds number is presented. The full-order model, on which the Galerkin projection is applied, is based on a…
We propose a procedure for the numerical approximation of invariance equations arising in the moment matching technique associated with reduced-order modeling of high-dimensional dynamical systems. The Galerkin residual method is employed…
This paper presents a structure-preserving model reduction framework for linear systems, in which the $\mathcal{H}_2$ optimization is incorporated with the Petrov-Galerkin projection to preserve structural features of interest, including…
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,…
We consider a second-order linear system of ordinary differential equations (ODEs) including random variables. A stochastic Galerkin method yields a larger deterministic linear system of ODEs. We apply a model order reduction (MOR) of this…