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A systematic approach to nonlinear model order reduction (NMOR) of coupled fluid-structureflight dynamics systems of arbitrary fidelity is presented. The technique employs a Taylor series expansion of the nonlinear residual around…

Computational Engineering, Finance, and Science · Computer Science 2026-04-16 Nikolaos D. Tantaroudas , Ilias Karachalios

We study projection-free methods for constrained Riemannian optimization. In particular, we propose the Riemannian Frank-Wolfe (RFW) method. We analyze non-asymptotic convergence rates of RFW to an optimum for (geodesically) convex…

Optimization and Control · Mathematics 2021-11-29 Melanie Weber , Suvrit Sra

A Riemannian gradient descent algorithm and a truncated variant are presented to solve systems of phaseless equations $|Ax|^2=y$. The algorithms are developed by exploiting the inherent low rank structure of the problem based on the…

Numerical Analysis · Mathematics 2018-09-11 Jian-Feng Cai , Ke Wei

This paper studies large-scale optimization problems on Riemannian manifolds whose objective function is a finite sum of negative log-probability losses. Such problems arise in various machine learning and signal processing applications. By…

Optimization and Control · Mathematics 2022-07-18 Jiang Hu , Ruicheng Ao , Anthony Man-Cho So , Minghan Yang , Zaiwen Wen

We propose an extremely versatile approach to address a large family of matrix nearness problems, possibly with additional linear constraints. Our method is based on splitting a matrix nearness problem into two nested optimization problems,…

Numerical Analysis · Mathematics 2025-08-14 Miryam Gnazzo , Vanni Noferini , Lauri Nyman , Federico Poloni

In this paper, we present a projection-based model-order reduction (MOR) technique for smoothed particle hydrodynamics (SPH) simulations, which is a mesh-free approach within the Lagrangian framework. Our approach utilizes the proper…

Computational Physics · Physics 2025-07-29 Lidong Fang , Zilong Song , Kirk Fraser , Faisal Habib , Christopher Drummond , Huaxiong Huang

A non-intrusive model order reduction (MOR) method for solving parameterized electromagnetic scattering problems is proposed in this paper. A database collecting snapshots of high-fidelity solutions is built by solving the parameterized…

Numerical Analysis · Mathematics 2022-07-19 Xiao-Feng He , Liang Li , Stephane Lanteri , Kun Li

In this paper we discuss a projection model order reduction (MOR) method for a class of parametric linear evolution PDEs, which is based on the application of the Laplace transform. The main advantage of this approach consists in the fact…

Numerical Analysis · Mathematics 2022-09-02 Nicola Guglielmi , Mattia Manucci

A variational formulation of accelerated optimization on normed spaces was recently introduced by considering a specific family of time-dependent Bregman Lagrangian and Hamiltonian systems whose corresponding trajectories converge to the…

Optimization and Control · Mathematics 2022-01-11 Valentin Duruisseaux , Melvin Leok

The field of model order reduction (MOR) is growing in importance due to its ability to extract the key insights from complex simulations while discarding computationally burdensome and superfluous information. We provide an overview of MOR…

Nuclear Theory · Physics 2022-09-14 J. A. Melendez , C. Drischler , R. J. Furnstahl , A. J. Garcia , Xilin Zhang

We formulate here an approach to model reduction that is well-suited for linear time-invariant control systems that are stabilizable and detectable but may otherwise be unstable. We introduce a modified $\mathcal{H}_2$-error metric, the…

Numerical Analysis · Mathematics 2019-10-01 Tobias Breiten , Chris A. Beattie , Serkan Gugercin

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

In this work, we focus on reduced order modeling (ROM) techniques for hyperbolic conservation laws with application in uncertainty quantification (UQ) and in conjunction with the well-known Monte Carlo sampling method. Because we are…

Numerical Analysis · Mathematics 2018-08-13 R. Crisovan , D. Torlo , R. Abgrall , S. Tokareva

In this paper, we bring together the worlds of model order reduction for stochastic linear systems and $\mathcal H_2$-optimal model order reduction for deterministic systems. In particular, we supplement and complete the theory of error…

Numerical Analysis · Mathematics 2020-07-21 Martin Redmann , Melina A. Freitag

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

Riemannian submanifold optimization with momentum is computationally challenging because, to ensure that the iterates remain on the submanifold, we often need to solve difficult differential equations. Here, we simplify such difficulties…

Machine Learning · Statistics 2024-03-19 Wu Lin , Valentin Duruisseaux , Melvin Leok , Frank Nielsen , Mohammad Emtiyaz Khan , Mark Schmidt

The techniques and analysis presented in this paper provide new methods to solve optimization problems posed on Riemannian manifolds. A new point of view is offered for the solution of constrained optimization problems. Some classical…

Optimization and Control · Mathematics 2018-04-12 Steven Thomas Smith

This paper focuses on exploring efficient ways to find $\mathcal{H}_2$ optimal Structure-Preserving Model Order Reduction (SPMOR) of the second-order systems via interpolatory projection-based method Iterative Rational Krylov Algorithm…

Optimization and Control · Mathematics 2023-10-10 Md. Motlubar Rahman , M. Monir Uddin , L. S. Andallah , Mahtab Uddin

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

In post--layout circuit simulation, efficient model order reduction (MOR) for many--port resistor--capacitor (RC) circuits remains a crucial issue. The current mainstream MOR methods for such circuits include high--order moment matching…

Systems and Control · Electrical Eng. & Systems 2025-10-21 Siyuan Yin , Yuncheng Xu , Lin Liu , Fan Yang , Xuan Zeng , Chengtao An , Yangfeng Su