Related papers: A unifying framework for tangential interpolation …
This paper examines the construction of rth-order truncated balanced realizations via tangential interpolation at r specified interpolation points. It is demonstrated that when the truncated Hankel singular values are negligible-that is,…
A structure preserving proper orthogonal decomposition reduce-order modeling approach has been developed in [Gong et al. 2017] for the Hamiltonian system, which uses the traditional framework of Galerkin projection-based model reduction but…
In this paper we present a novel framework for obtaining high-order numerical methods for scalar conservation laws in one-space dimension for both the homogeneous and non-homogeneous case. The numerical schemes for these two settings are…
Parametric model order reduction by matrix interpolation allows for efficient prediction of the behavior of dynamic systems without requiring knowledge about the underlying parametric dependency. Within this approach, reduced models are…
This manuscript addresses the analysis and design of feedback laws for the stabilization of bilinear control systems in infinite-dimensional spaces. It first examines weak, strong, and polynomial stabilization within a Hilbert space…
An adaptive parametric reduced-order modeling method based on interpolating poles of reduced-order models is proposed in this paper. To guarantee correct interpolation, a pole-matching process is conducted to determine which poles of two…
Interpolation models are critical for a wide range of applications, from numerical optimization to artificial intelligence. The reliability of the provided interpolated value is of utmost importance, and it is crucial to avoid the…
Direct numerical simulation of dynamical systems is of fundamental importance in studying a wide range of complex physical phenomena. However, the ever-increasing need for accuracy leads to extremely large-scale dynamical systems whose…
In this paper, we propose two methods for multivariate Hermite interpolation of manifold-valued functions. On the one hand, we approach the problem via computing suitable weighted Riemannian barycenters. To satisfy the conditions for…
One approach to parametric and adaptive model reduction is via the interpolation of orthogonal bases, subspaces or positive definite system matrices. In all these cases, the sampled inputs stem from matrix sets that feature a geometric…
Suppressing vibrations in mechanical systems, usually described by second-order dynamical models, is a challenging task in mechanical engineering in terms of computational resources even nowadays. One remedy is structure-preserving model…
In this paper we suggest a moment matching method for quadratic-bilinear dynamical systems. Most system-theoretic reduction methods for nonlinear systems rely on multivariate frequency representations. Our approach instead uses univariate…
Vibration and dissipation in vibro-acoustic systems can be assessed using frequency response analysis. Evaluating a frequency sweep on a full-order model can be very costly, so model order reduction methods are employed to compute…
It was recently shown that the theory of linear stochastic systems can be viewed as a particular case of the theory of linear systems on a certain commutative ring of power series in a countable number of variables. In the present work we…
We develop the interpolatory $\mathcal{H}_2$ optimal model reduction framework for linear control systems posed on infinite dimensional state, input and output spaces. Specifically, we consider linear systems formulated as controlled…
We propose a projection based multi-moment matching method for model order reduction of quadratic-bilinear systems. The goal is to construct a reduced system that ensures higher-order moment matching for the multivariate transfer functions…
In video super-resolution, it is common to use a frame-wise alignment to support the propagation of information over time. The role of alignment is well-studied for low-level enhancement in video, but existing works overlook a critical step…
We present a nonlinear interpolation technique for parametric fields that exploits optimal transportation of coherent structures of the solution to achieve accurate performance. The approach generalizes the nonlinear interpolation procedure…
This paper addresses problems on the structural design of control systems taking explicitly into consideration the possible application to large-scale systems. We provide an efficient and unified framework to solve the following major…
When balanced truncation is used for model order reduction, one has to solve a pair of Lyapunov equations for two Gramians and uses them to construct a reduced-order model. Although advances in solving such equations have been made, it is…