Related papers: Nonlinear balanced truncation model reduction thro…
Many reduced order models are neither robust with respect to the parameter changes nor cost-effective enough for handling the nonlinear dependence of complex dynamical systems. In this study, we put forth a robust machine learning framework…
Model order reduction (MOR) is often applied to spatially-discretized partial differential equations to reduce their order and hence decrease computational complexity. A reduced system can be obtained, e.g., by time-limited balanced…
Model order reduction algorithms for large-scale descriptor systems are proposed using balanced truncation, in which symmetry or block skew symmetry (reciprocity) and the positive realness of the original transfer matrix are preserved. Two…
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…
Model order reduction plays a crucial role in simplifying complex systems while preserving their essential dynamic characteristics, making it an invaluable tool in a wide range of applications, including robotic systems, signal processing,…
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…
In many areas of engineering, nonlinear numerical analysis is playing an increasingly important role in supporting the design and monitoring of structures. Whilst increasing computer resources have made such formerly prohibitive analyses…
In this paper, we investigate a large-scale stochastic system with bilinear drift and linear diffusion term. Such high dimensional systems appear for example when discretizing a stochastic partial differential equations in space. We study a…
This paper introduces a quadrature-free, non-intrusive approach to balanced truncation for both continuous-time and discrete-time systems. The method non-intrusively constructs reduced-order models using available transfer function samples…
Model reduction is a central topic in systems biology and dynamical systems theory, for reducing the complexity of detailed models, finding important parameters, and developing multi-scale models for instance. While perturbation theory is a…
When solving partial differential equations numerically, usually a high order spatial discretisation is needed. Model order reduction (MOR) techniques are often used to reduce the order of spatially-discretised systems and hence reduce…
A standard approach for model reduction of linear input-output systems is balanced truncation, which is based on the controllability and observability properties of the underlying system. The related dominant subspace projection model…
We deduce a procedure to apply balanced truncation to parameter-dependent differential-algebraic systems. For that we solve multiple projected Lyapunov equations for different parameter values to compute the Gramians that are required for…
We provide an analytical framework for balanced realization model order reduction of linear control systems which depend on an unknown parameter. Besides recovering known results for the first order corrections, we obtain explicit novel…
As a special type of bilinear systems, K-power bilinear systems possess a special coupled structure along with nice properties in practice. In this paper, we investigate the data-driven counterpart of balanced truncation for K-power…
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 present a scalable approach to computing nonlinear balancing energy functions for control-affine systems with polynomial nonlinearities. Al'brekht's power-series method is used to solve the Hamilton-Jacobi-Bellman equations for…
We consider linear magneto-quasistatic field equations which arise in simulation of low-frequency electromagnetic devices coupled to electrical circuits. A finite element discretization of such equations on 3D domains leads to a singular…
In some previous works, two of the authors introduced a technique to design high-order numerical methods for one-dimensional balance laws that preserve all their stationary solutions. The basis of these methods is a well-balanced…
This work discusses model reduction for differential-algebraic systems with quadratic output equations. Under mild conditions, these systems can be transformed into a Weierstra{\ss} canonical form and, thus, be decoupled into differential…