Related papers: Data-Driven Model Reduction by Moment Matching for…
We introduce a data-driven order reduction method for nonlinear control systems, drawing on recent progress in machine learning and statistical dimensionality reduction. The method rests on the assumption that the nonlinear system behaves…
In this paper, a parametric model order reduction (pMOR) technique is proposed to find a simplified system representation of a large-scale and complex thermal system. The main principle behind this technique is that any change of the…
Motivated by a recently proposed error estimator for the transfer function of the reduced-order model of a given linear dynamical system, we further develop more theoretical results in this work. Furthermore, we propose several variants of…
In this paper we study the problem of model reduction of linear network systems. We aim at computing a reduced order stable approximation of the network with the same topology and optimal w.r.t. H2 norm error approximation. Our approach is…
We present a novel method for learning reduced-order models of dynamical systems using nonlinear manifolds. First, we learn the manifold by identifying nonlinear structure in the data through a general representation learning problem. The…
We introduce the Vector Fitting algorithm for the creation of reduced-order models from the sampled response of a linear time-invariant system. This data-driven approach to reduction is particularly useful when the system under modeling is…
We provide a unifying framework for $\mathcal{L}_2$-optimal reduced-order modeling for linear time-invariant dynamical systems and stationary parametric problems. Using parameter-separable forms of the reduced-model quantities, we derive…
In this paper, the moment matching techniques are adopted to obtain reduced-order closed-loop systems with reduced-order controllers that maintain the closed-loop stability and guarantee desired asymptotic performance, after revealing the…
Model selection methods are used in different scientific contexts to represent a characteristic data set in terms of a reduced number of parameters. Apparently, these methods have not found their way into the literature on multibody systems…
The dynamic mode decomposition (DMD) is a data-driven method used for identifying the dynamics of complex nonlinear systems. It extracts important characteristics of the underlying dynamics using measured time-domain data produced either by…
Systems may depend on parameters which one may control, or which serve to optimise the system, or are imposed externally, or they could be uncertain. This last case is taken as the ``Leitmotiv'' for the following. A reduced order model is…
Projection-based reduced order models are effective at approximating parameter-dependent differential equations that are parametrically separable. When parametric separability is not satisfied, which occurs in both linear and nonlinear…
A method for model reduction in nonlinear ODE systems is demonstrated through computational examples. The method does not require an implicit separation of time-scales in the fine dynamics to be effective. From the computational standpoint,…
We propose a new model reduction framework for problems that exhibit transport phenomena. As in the moving finite element method (MFEM), our method employs time-dependent transformation operators and, especially, generalizes MFEM to…
In this paper, we compute a low order approximation of a system of large order $n$ that matches $\nu$ moments of order $j_i$ of the transfer function, at $\nu$ interpolation points, has $\ell$ poles and $k$ zeros fixed and also matches…
Piecewise-linear nonlinear systems appear in many engineering disciplines. Prediction of the dynamic behavior of such systems is of great importance from practical and theoretical viewpoint. In this paper, a data-driven model order…
Reduced order modeling has gained considerable attention in recent decades owing to the advantages offered in reduced computational times and multiple solutions for parametric problems. The focus of this manuscript is the application of…
Model order reduction techniques simplify high-dimensional dynamical systems by deriving lower-dimensional models that retain essential system characteristics. These techniques are crucial for the controller design of complex systems while…
The reduction of dynamical systems has a rich history, with many important applications related to stability, control and verification. Reduction of nonlinear systems is typically performed in an exact manner - as is the case with…
We propose a data-driven model order reduction (MOR) technique for parametrized partial differential equations that exhibit parameter-dependent jump-discontinuities. Such problems have poor-approximability in a linear space and therefore,…