Related papers: $\mathcal{H}_2$-Optimal Model Reduction Using Proj…
We consider the problem of locating a nearest descriptor system of prescribed reduced order to a descriptor system with large order with respect to the ${\mathcal L}_\infty$ norm. Widely employed approaches such as the balanced truncation…
The matrix factor model has drawn growing attention for its advantage in achieving two-directional dimension reduction simultaneously for matrix-structured observations. In this paper, we propose a simple iterative least squares algorithm…
In the time- and frequency-limited model order reduction, a reduced-order approximation of the original high-order model is sought to ensure superior accuracy in some desired time and frequency intervals. We first consider the time-limited…
We propose a novel online learning paradigm for nonlinear-function estimation tasks based on the iterative projections in the L2 space with probability measure reflecting the stochastic property of input signals. The proposed learning…
This paper proposes several novel optimization algorithms for minimizing a nonlinear objective function. The algorithms are enlightened by the optimal state trajectory of an optimal control problem closely related to the minimized objective…
The adaptive Antoulas-Anderson (AAA) algorithm for rational approximation is a widely used method for the efficient construction of highly accurate rational approximations to given data. While AAA can often produce rational approximations…
Given a set of response observations for a parametrized dynamical system, we seek a parametrized dynamical model that will yield uniformly small response error over a range of parameter values yet has low order. Frequently, access to…
Reduced modeling of a computationally demanding dynamical system aims at approximating its trajectories, while optimizing the trade-off between accuracy and computational complexity. In this work, we propose to achieve such an approximation…
Adaptive cubic regularization methods for solving nonconvex problems need the efficient computation of the trial step, involving the minimization of a cubic model. We propose a new approach in which this model is minimized in a low…
We investigate the use of inexact solves for interpolatory model reduction and consider associated perturbation effects on the underlying model reduction problem. We give bounds on system perturbations induced by inexact solves and relate…
In this effort we propose a data-driven learning framework for reduced order modeling of fluid dynamics. Designing accurate and efficient reduced order models for nonlinear fluid dynamic problems is challenging for many practical…
The structural properties of mechanical metamaterials are typically studied with two-scale methods based on computational homogenization. Because such materials have a complex microstructure, enriched schemes such as second-order…
Derivative-free optimization methods are numerical methods for optimization problems in which no derivative information is used. Such optimization problems are widely seen in many real applications. One particular class of derivative-free…
In this contribution we develop an efficient reduced order model for solving parametrized linear-quadratic optimal control problems with linear time-varying state system. The fully reduced model combines reduced basis approximations of the…
For approximately solving linear ill-posed problems in Hilbert spaces, we investigate the regularization properties of the aggregation method and the RatCG method. These recent algorithms use previously calculated solutions of Tikhonov…
This paper studies the model order reduction of second-order index-1 descriptor systems using a tangential interpolation projection method based on the Iterative Rational Krylov Algorithm (IRKA). Our primary focus is to reduce the system…
Random projections or sketching are widely used in many algorithmic and learning contexts. Here we study the performance of iterative Hessian sketch for least-squares problems. By leveraging and extending recent results from random matrix…
We propose a new Iteratively Reweighted Least Squares (IRLS) algorithm for the problem of completing or denoising low-rank matrices that are structured, e.g., that possess a Hankel, Toeplitz or block-Hankel/Toeplitz structure. The algorithm…
We study randomized sketching methods for approximately solving least-squares problem with a general convex constraint. The quality of a least-squares approximation can be assessed in different ways: either in terms of the value of the…
Although design optimization has shown its great power of automatizing the whole design process and providing an optimal design, using sophisticated computational models, its process can be formidable due to a computationally expensive…