Related papers: Frequency-limited H$_2$ Model Order Reduction Base…
A general method for accelerating fixed point schemes for problems related to partial differential equations is presented in this article. The speedup is obtained by training a reduced-order model on-the-fly, removing the need to do an…
This paper presents an H2-optimal model order reduction (MOR) method for linear systems with quadratic outputs based on Riemannian optimization. The H2-optimal MOR is formulated as an optimization problem in which the optimization variables…
Model predictive control is a powerful framework for enabling optimal control of constrained systems. However, for systems that are described by high-dimensional state spaces this framework can be too computationally demanding for real-time…
Mechanical systems are often characterized only by their response to certain loads known from experiments or simulations. The obtained data can be used for various purposes: system analysis, design of mathematical models, or construction of…
This paper addresses frequency regulation under operational constraints in interconnected power systems with high penetration of inverter-based renewable generation. A two-layer control architecture is proposed that combines optimized droop…
Considering the use of dynamical systems in practical applications, often only limited regions in the time or frequency domain are of interest. Therefor, it usually pays off to compute local approximations of the used dynamical systems in…
The dynamic behavior of jointed assemblies exhibiting friction nonlinearities features amplitude-dependent dissipation and stiffness. To develop numerical simulations for predictive and design purposes, macro-scale High Fidelity Models…
Although projection-based reduced-order models (ROMs) for parameterized nonlinear dynamical systems have demonstrated exciting results across a range of applications, their broad adoption has been limited by their intrusivity: implementing…
In a wide range of applications it is desirable to optimally control a dynamical system with respect to concurrent, potentially competing goals. This gives rise to a multiobjective optimal control problem where, instead of computing a…
For the $h$-finite-element method ($h$-FEM) applied to the Helmholtz equation, the question of how quickly the meshwidth $h$ must decrease with the frequency $k$ to maintain accuracy as $k$ increases has been studied since the mid 80's.…
We propose a randomized a posteriori error estimator for reduced order approximations of parametrized (partial) differential equations. The error estimator has several important properties: the effectivity is close to unity with prescribed…
This paper is an attempt to remedy the problem of slow convergence for first-order numerical algorithms by proposing an adaptive conditioning heuristic. First, we propose a parallelizable numerical algorithm that is capable of solving…
A standard approach to reduced-order modeling of higher-order linear dynamical systems is to rewrite the system as an equivalent first-order system and then employ Krylov-subspace techniques for reduced-order modeling of first-order…
We derive a model problem for quasicontinuum approximations that allows a simple, yet insightful, analysis of the optimal-order convergence rate in the continuum limit for both the energy-based quasicontinuum approximation and the…
We give a goal-oriented a posteriori error estimator for the atomistic-continuum modeling error in the quasicontinuum method, and we use this estimator to design an adaptive algorithm to compute a quantity of interest to a given tolerance…
Probability estimation is an elementary building block of every statistical data compression algorithm. In practice probability estimation is often based on relative letter frequencies which get scaled down, when their sum is too large.…
Systems may depend on parameters which one may control, or which serve to optimise the system, or are imposed externally, or they could be uncertain. This last case is taken as the ``Leitmotiv'' for the following. A reduced order model is…
In this paper, we study the fundamental open question of finding the optimal high-order algorithm for solving smooth convex minimization problems. Arjevani et al. (2019) established the lower bound $\Omega\left(\epsilon^{-2/(3p+1)}\right)$…
The primary focus of this paper is on designing an inexact first-order algorithm for solving constrained nonlinear optimization problems. By controlling the inexactness of the subproblem solution, we can significantly reduce the…
Parametric high-fidelity simulations are of interest for a wide range of applications. But the restriction of computational resources renders such models to be inapplicable in a real-time context or in multi-query scenarios. Model order…