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In this paper we compute families of reduced order models that match a prescribed set of moments of a highly dimensional linear time-invariant system. First, we fully parametrize the models in the interpolation points and in the free…

Optimization and Control · Mathematics 2018-11-20 I. Necoara , T. C. Ionescu

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…

Numerical Analysis · Mathematics 2024-08-29 Hendrik Kleikamp , Lukas Renelt

Feedback control synthesis for nonlinear, parameter-dependent fluid flow control problems is considered. The optimal feedback law requires the solution of the Hamilton-Jacobi-Bellman (HJB) PDE suffering the curse of dimensionality. This is…

Optimization and Control · Mathematics 2023-11-29 Sergey Dolgov , Dante Kalise , Luca Saluzzi

In this paper, we study linearly constrained policy optimization over the manifold of Schur stabilizing controllers, equipped with a Riemannian metric that emerges naturally in the context of optimal control problems. We provide extrinsic…

Optimization and Control · Mathematics 2023-10-27 Shahriar Talebi , Mehran Mesbahi

Optimal transport (OT) has recently found widespread interest in machine learning. It allows to define novel distances between probability measures, which have shown promise in several applications. In this work, we discuss how to…

Machine Learning · Computer Science 2021-10-11 Bamdev Mishra , N T V Satyadev , Hiroyuki Kasai , Pratik Jawanpuria

Model order reduction (MOR) techniques are often used to reduce the order of spatially-discretized (stochastic) partial differential equations and hence reduce computational complexity. A particular class of MOR techniques is balancing…

Optimization and Control · Mathematics 2019-03-29 Martin Redmann

We develop optimization-based structure-preserving model order reduction (MOR) methods for port-Hamiltonian (pH) descriptor systems of differentiation index one. Descriptor systems in pH form permit energy-based modeling and intuitive…

Optimization and Control · Mathematics 2022-06-06 Paul Schwerdtner , Tim Moser , Volker Mehrmann , Matthias Voigt

We present a technique for the approximation of a class of Hilbert space-valued maps which arise within the framework of Model Order Reduction for parametric partial differential equations, whose solution map has a meromorphic structure.…

Numerical Analysis · Mathematics 2021-02-19 Davide Pradovera

Multi-Output Regression (MOR) has been widely used in scientific data analysis for decision-making. Unlike traditional regression models, MOR aims to simultaneously predict multiple real-valued outputs given an input. However, the…

Machine Learning · Computer Science 2024-10-22 Renyuan Li , Zhehui Chen , Guanyi Wang

Frequency-limited model order reduction aims to approximate a high-order model with a reduced-order model that maintains high fidelity within a specific frequency range. Beyond this range, a decrease in accuracy is acceptable due to the…

Systems and Control · Electrical Eng. & Systems 2023-06-27 Umair Zulfiqar , Xin Du , Qiuyan Song , Zhi-Hua Xiao , Victor Sreeram

Optimization under the symplecticity constraint is an approach for solving various problems in quantum physics and scientific computing. Building on the results that this optimization problem can be transformed into an unconstrained problem…

Optimization and Control · Mathematics 2024-06-21 Bin Gao , Nguyen Thanh Son , Tatjana Stykel

This paper provides an $H_2$ optimal scheme for reducing diffusively coupled second-order systems evolving over undirected networks. The aim is to find a reduced-order model that not only approximates the input-output mapping of the…

Optimization and Control · Mathematics 2021-11-18 Lanlin Yu , Xiaodong Cheng , Jacquelien M. A. Scherpen , Junlin Xiong

In this work, we study projection-based model order reduction (MOR) for switched linear systems (SLS) in control form, where the projection matrices are obtained from the solutions of generalized Lyapunov equations (GLEs). We investigate…

Numerical Analysis · Mathematics 2026-05-18 Mattia Manucci , Benjamin Unger

We develop a method for optimization in shape spaces, i.e., sets of surfaces modulo re-parametrization. Unlike previously proposed gradient flows, we achieve superlinear convergence rates through a subtle approximation of the shape Hessian,…

Computer Vision and Pattern Recognition · Computer Science 2014-04-15 J. Balzer , S. Soatto

Numerous problems in optics, quantum physics, stability analysis, and control of dynamical systems can be brought to an optimization problem with matrix variable subjected to the symplecticity constraint. As this constraint nicely forms a…

Optimization and Control · Mathematics 2022-11-18 Bin Gao , Nguyen Thanh Son , Tatjana Stykel

In this paper, we generalize existing frameworks for $\mathcal{H}_2\otimes\mathcal{L}_2$-optimal model order reduction to a broad class of parametric linear time-invariant systems. To this end, we derive first-order necessary ptimality…

Optimization and Control · Mathematics 2022-04-04 Manuela Hund , Tim Mitchell , Petar Mlinarić , Jens Saak

In probabilistic modeling, parameter estimation is commonly formulated as a minimization problem on a parameter manifold. Optimization in such spaces requires geometry-aware methods that respect the underlying information structure. While…

Computation · Statistics 2025-11-17 Derun Zhou , Keisuke Yano , Mahito Sugiyama

In this paper, the problems of frequency-limited and time-limited H2-optimal model order reduction of linear time-invariant systems are considered within the oblique projection framework. It is shown that it is inherently not possible to…

Systems and Control · Electrical Eng. & Systems 2021-09-15 Umair Zulfiqar , Victor Sreeram , Xin Du

The $\mathcal{H}_2$ model reduction problem for high-dimensional linear quantum systems is studied under the constraint of physical realizability (PR). This constraint requires preservation of the canonical commutation relations and the…

Quantum Physics · Physics 2026-05-11 Alfo Borzi , Guofeng Zhang

In this paper, we consider model order reduction (MOR) methods for problems with slowly decaying Kolmogorov $n$-widths as, e.g., certain wave-like or transport-dominated problems. To overcome this Kolmogorov barrier within MOR, nonlinear…

Numerical Analysis · Mathematics 2025-01-08 Silke Glas , Benjamin Unger