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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 propose a novel reduced-rank adaptive filtering algorithm by blending the idea of the Krylov subspace methods with the set-theoretic adaptive filtering framework. Unlike the existing Krylov-subspace-based reduced-rank…

Reduced order models, in particular the reduced basis method, rely on empirically built and problem dependent basis functions that are constructed during an off-line stage. In the on-line stage, the precomputed problem-dependent solution…

This paper proposes a data-driven algorithm for model order reduction (MOR) of large-scale wind farms and studies the effects that the obtained reduced-order model (ROM) has when this is integrated into the power grid. With respect to…

This paper constructs adaptive sparse grid collocation method onto arbitrary order piecewise polynomial space. The sparse grid method is a popular technique for high dimensional problems, and the associated collocation method has been well…

We present an adaptive reduced-order model for the efficient time-resolved simulation of fluid-structure interaction problems with complex and non-linear deformations. The model is based on repeated linearizations of the structural balance…

We address the problem of reasoning about interleavings in safety verification of concurrent programs. In the literature, there are two prominent techniques for pruning the search space. First, there are well-investigated trace-based…

The objective of this paper is to develop a global non-intrusive Parametric Model Order Reduction (PMOR) methodology for the problem of changing well locations in an oil field, that can eventually be used for well placement optimization to…

Understanding when and why interpolating methods generalize well has recently been a topic of interest in statistical learning theory. However, systematically connecting interpolating methods to achievable notions of optimality has only…

A methodology grounded in model reduction is presented for accelerating the gradient-based solution of a family of linear or nonlinear constrained optimization problems where the constraints include at least one linear Partial Differential…

The ab initio description of the spectral interior of the absorption spectrum poses both a theoretical and computational challenge for modern electronic structure theory. Due to the often spectrally dense character of this domain in the…

Parameter-dependent models arise in many contexts such as uncertainty quantification, sensitivity analysis, inverse problems or optimization. Parametric or uncertainty analyses usually require the evaluation of an output of a model for many…

The current implementation of Thiele rational interpolation in Maple (the ThieleInterpolation routine) breaks down when the points are not well-ordered. In this article, it is shown how this breakdown can be avoided by ordering the…

This work proposes novel techniques for the efficient numerical simulation of parameterized, unsteady partial differential equations. Projection-based reduced order models (ROMs) such as the reduced basis method employ a (Petrov-)Galerkin…

We investigate a suitable application of Model Order Reduction (MOR) techniques for the numerical approximation of Turing patterns, that are stationary solutions of reaction-diffusion PDE (RD-PDE) systems. We show that solutions of…

In this contribution, we propose a detailed study of interpolation-based data-driven methods that are of relevance in the model reduction and also in the systems and control communities. The data are given by samples of the transfer…

The paper introduces a reduced order model (ROM) for numerical integration of a dynamical system which depends on multiple parameters. The ROM is a projection of the dynamical system on a low dimensional space that is both problem-dependent…

In dynamical system theory, the process of obtaining a reduced-order approximation of the high-order model is called model order reduction. The closeness of the reduced-order model to the original model is generally gauged by using system…

This paper presents a novel, more efficient proper orthogonal decomposition (POD) based reduced-order model (ROM) for compressible flows. In this POD model the governing equations, i.e., the conservation of mass, momentum, and energy…

In this paper, we present an adaptive framework for constructing a pseudo-optimal reduced model for the frequency-limited H2-optimal model order reduction problem. We show that the frequency-limited pseudo-optimal reduced-order model has an…