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In this paper we study the problem of model reduction of linear network systems. We aim at computing a reduced order stable approximation of the network with the same topology and optimal w.r.t. H2 norm error approximation. Our approach is…

Optimization and Control · Mathematics 2019-05-21 I. Necoara , T. C. Ionescu

We analyze a posteriori error bounds for stabilized finite element discretizations of second-order steady-state mean field games. We prove the local equivalence between the $H^1$-norm of the error and the dual norm of the residual. We then…

Numerical Analysis · Mathematics 2025-12-02 Yohance A. P. Osborne , Iain Smears , Harry Wells

Prediction via deterministic continuous-time models will always be subject to model error, for example due to unexplainable phenomena, uncertainties in any data driving the model, or discretisation/resolution issues. In this paper, we build…

Dynamical Systems · Mathematics 2025-06-30 Liam Blake , John Maclean , Sanjeeva Balasuriya

We address the design of a model predictive control (MPC) scheme for large-scale linear systems using reduced-order models (ROMs). Our approach uses a ROM, leverages tools from robust control, and integrates them into an MPC framework to…

Systems and Control · Electrical Eng. & Systems 2026-03-24 Johannes Köhler , Carlo Scholz , Melanie Zeilinger

This article derives lower bounds on the convergence rate of continuous-time gradient-based optimization algorithms. The algorithms are subjected to a time-normalization constraint that avoids a reparametrization of time in order to make…

Optimization and Control · Mathematics 2020-08-04 Michael Muehlebach , Michael I. Jordan

A reliable model order reduction process for parametric analysis in electromagnetics is detailed. Special emphasis is placed on certifying the accuracy of the reduced-order model. For this purpose, a sharp state error estimator is proposed.…

Numerical Analysis · Mathematics 2023-04-04 Sridhar Chellappa , Lihong Feng , Valentin de la Rubia , Peter Benner

A classical reduced order model for dynamical problems involves spatial reduction of the problem size. However, temporal reduction accompanied by the spatial reduction can further reduce the problem size without losing accuracy much, which…

Numerical Analysis · Mathematics 2019-10-04 Youngsoo Choi , Peter Brown , Bill Arrighi , Robert Anderson

A class of linear parabolic equations are considered. We give a posteriori error estimates in the maximum norm for a method that comprises extrapolation applied to the backward Euler method in time and finite element discretisations in…

Numerical Analysis · Mathematics 2022-08-18 Torsten Linß , Goran Radojev

We present new tight bounds for averaging differential inclusions, which we apply to multi-frequency inclusions consisting of a sum of time periodic set-valued mappings. For this family of inclusions we establish an a tight estimate of…

Optimization and Control · Mathematics 2014-03-11 Ido Bright

This paper studies model order reduction of multi-agent systems consisting of identical linear passive subsystems, where the interconnection topology is characterized by an undirected weighted graph. Balanced truncation based on a pair of…

Optimization and Control · Mathematics 2019-01-29 Xiaodong Cheng , Jacquelien M. A. Scherpen , Bart Besselink

This paper presents uniform-in-time finite-sample bounds for regularized linear regression with vector-valued outputs and conditionally zero-mean subgaussian noise. By revisiting classical self-normalized martingale arguments, we obtain…

Statistics Theory · Mathematics 2026-03-20 Léo Simpson , Katrin Baumgärtner , Johannes Köhler , Moritz Diehl

We consider the unilateral contact problem between an elastic body and a rigid foundation in a description that includes both Tresca and Coulomb friction conditions. For this problem, we present an a posteriori error analysis based on an…

Numerical Analysis · Mathematics 2024-01-08 Ilaria Fontana , Daniele A. Di Pietro

This work focuses on numerical solutions of optimal control problems. A time discretization error representation is derived for the approximation of the associated value function. It concerns Symplectic Euler solutions of the Hamiltonian…

Optimization and Control · Mathematics 2016-02-23 Jesper Karlsson , Stig Larsson , Mattias Sandberg , Anders Szepessy , Raùl Tempone

The paper is concerned with guaranteed a posteriori error estimates for a class of evolutionary problems related to poroelastic media governed by the quasi-static linear Biot equations. The system is decoupled employing the fixed-stress…

Numerical Analysis · Mathematics 2020-01-22 Kundan Kumar , Svetlana Kyas , Jan Nordbotten , Sergey Repin

Reduced order models are computationally inexpensive approximations that capture the important dynamical characteristics of large, high-fidelity computer models of physical systems. This paper applies machine learning techniques to improve…

Machine Learning · Computer Science 2015-11-11 Azam Moosavi , Razvan Stefanescu , Adrian Sandu

Simulating quantum dynamics beyond the reach of classical computers is one of the main envisioned applications of quantum computers. The most promising quantum algorithms to this end in the near-term are the simplest, which use the Trotter…

Quantum Physics · Physics 2022-05-25 David Layden

In this paper, we consider the problem of controlling a dynamical system such that its trajectories satisfy a temporal logic property in a given amount of time. We focus on multi-affine systems and specifications given as syntactically…

Systems and Control · Computer Science 2012-03-27 Ebru Aydin Gol , Calin Belta

We introduce an algorithm based on a method of snapshots for computing approximate balanced truncations for discrete-time, stable, linear time-periodic systems. By construction, this algorithm is applicable to very high-dimensional systems,…

Optimization and Control · Mathematics 2007-08-06 Zhanhua Ma , Clarence W. Rowley , Gilead Tadmor

In this work, we aim at efficiently solving a parametrized family of optimal transport problems by using model order reduction methods. We propose a reduced-order model by adding to the primal (respectively dual) version of the…

Numerical Analysis · Mathematics 2026-04-13 Elise Bonnet-Weill , Virginie Ehrlacher , Luca Nenna

In this work we propose tailored model order reduction for varying boundary optimal control problems governed by parametric partial differential equations. With varying boundary control, we mean that a specific parameter changes where the…

Numerical Analysis · Mathematics 2024-01-22 Maria Strazzullo , Fabio Vicini