Related papers: Model Reduction by Rational Interpolation

We consider the reduction of parametric families of linear dynamical systems having an affine parameter dependence that differ from one another by a low-rank variation in the state matrix. Usual approaches for parametric model reduction…

We propose new linear combinations of compositions of a basic second-order scheme with appropriately chosen coefficients to construct higher order numerical integrators for differential equations. They can be considered as a generalization…

The root mean squared error is an important measure used in a variety of applications such as structural dynamics and acoustics to model averaged deviations from standard behavior. For large-scale systems, simulations of this quantity…

The paper presents a novel model order reduction technique for large-scale linear parameter varying (LPV) systems. The approach is based on decoupling the original dynamics into smaller dimensional LPV subsystems that can be independently…

The simplest way to obtain continuous interpolation between two points in high dimensional space is to draw a line between them. While previous works focused on the general connectivity between model parameters, we explored linear…

We develop a unifying framework for interpolatory $\mathcal{L}_2$-optimal reduced-order modeling for a wide classes of problems ranging from stationary models to parametric dynamical systems. We first show that the framework naturally…

Estimates of the approximate factor model are increasingly used in empirical work. Their theoretical properties, studied some twenty years ago, also laid the ground work for analysis on large dimensional panel data models with cross-section…

In this paper, a practicable simulation-free model order reduction method by nonlinear moment matching is developed. Based on the steady-state interpretation of linear moment matching, we comprehensively explain the extension of this…

With the increasing popularity of deep learning in image processing, many learned lossless image compression methods have been proposed recently. One group of algorithms that have shown good performance are based on learned pixel-based…

It is often possible to perform reduced order modelling by specifying linear subspace which accurately captures the dynamics of the system. This approach becomes especially appealing when linear subspace explicitly depends on parameters of…

In this paper, we investigate interpolatory projection framework for model reduction of descriptor systems. With a simple numerical example, we first illustrate that employing subspace conditions from the standard state space settings to…

Multi-dimensional optimization is widely used in virtually all areas of modern astrophysics. However, it is often too computationally expensive to evaluate a model on-the-fly. Typically, it is solved by pre-computing a grid of models for a…

One of the very few mathematically rigorous nonlinear model reduction methods is the restriction of a dynamical system to a low-dimensional, sufficiently smooth, attracting invariant manifold. Such manifolds are usually found using local…

Recently, it has become evident that submodularity naturally captures widely occurring concepts in machine learning, signal processing and computer vision. Consequently, there is need for efficient optimization procedures for submodular…

Directional interpolation is a fast and efficient compression technique for high-frequency Helmholtz boundary integral equations, but it requires a very large amount of storage in its original form. Algebraic recompression can significantly…

In this work, we investigate a model order reduction scheme for high-fidelity nonlinear structured parametric dynamical systems. More specifically, we consider a class of nonlinear dynamical systems whose nonlinear terms are polynomial…

Computationally cheap yet accurate dynamical models are a key requirement for real-time capable nonlinear optimization and model-based control. When given a computationally expensive high-order prediction model, a reduction to a lower-order…

We consider the model reduction problem for linear time-invariant dynamical systems having nonzero (but otherwise indeterminate) initial conditions. Building upon the observation that the full system response is decomposable as a…

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…

A method is presented that reduces the number of terms of systems of linear equations (algebraic, ordinary and partial differential equations). As a byproduct these systems have a tendency to become partially decoupled and are more likely…