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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…
Controlling infinite dimensional models remains a challenging task for many practitioners since they are not suitable for traditional control design techniques or will result in a high-order controller too complex for implementation.…
This paper presents a structure-exploiting nonlinear model reduction method for systems with general nonlinearities. First, the nonlinear model is lifted to a model with more structure via variable transformations and the introduction of…
The Koopman framework is a popular approach to transform a finite dimensional nonlinear system into an infinite dimensional, but linear model through a lifting process, using so-called observable functions. While there is an extensive…
Steering a system towards a desired target in a very short amount of time is challenging from a computational standpoint. Indeed, the intrinsically iterative nature of optimal control problems requires multiple simulations of the physical…
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…
Multiple model reduction techniques have been proposed to tackle linear and non linear problems. Intrusive model order reduction techniques exhibit high accuracy levels, however, they are rarely used as a standalone industrial tool, because…
$\mathcal{H}_2$-optimal model order reduction algorithms represent a significant class of techniques, known for their accuracy, which has been extensively validated over the past two decades. Among these, the Iterative Rational Krylov…
The direct computation of the third-order normal form for a geometrically nonlinear structure discretised with the finite element (FE) method, is detailed. The procedure allows to define a nonlinear mapping in order to derive accurate…
This work proposes a Bayesian inference method for the reduced-order modeling of time-dependent systems. Informed by the structure of the governing equations, the task of learning a reduced-order model from data is posed as a Bayesian…
This paper presents a novel derivation of the direct parametrisation method for invariant manifolds able to build simulation-free reduced-order models for nonlinear piezoelectric structures, with a particular emphasis on applications to…
Reduced Order Modelling (ROM) has been widely used to create lower order, computationally inexpensive representations of higher-order dynamical systems. Using these representations, ROMs can efficiently model flow fields while using…
In this paper, we develop a nonlinear reduction framework based on our recently introduced extended group finite element method. By interpolating nonlinearities onto approximation spaces defined with the help of finite elements, the…
We investigate the use of reduced-order modelling to run discrete element simulations at higher speeds. Taking a data-driven approach, we run many offline simulations in advance and train a model to predict the velocity field from the mass…
Reduced order modeling has gained considerable attention in recent decades owing to the advantages offered in reduced computational times and multiple solutions for parametric problems. The focus of this manuscript is the application of…
We introduce a reduced order model (ROM) methodology for inverse electromagnetic wave scattering in layered lossy media, using data gathered by an antenna which generates a probing wave and measures the time resolved reflected wave. We…
In this paper, we address extensions of the Loewner Data-Driven Control (L-DDC) methodology. First, this approach is extended by incorporating two alternative approximation methods known as Adaptive-Antoulas-Anderson (AAA) and Vector…
We extend a localized model order reduction method for the distributed finite element solution of elliptic boundary value problems in the cloud. We give a computationally efficient technique to compute the required inner product matrices…
The paper presents a model reduction framework geared towards the analysis and design of systems that switch and oscillate. While such phenomena are ubiquitous in nature and engineering, model reduction methods are not well developed for…
Projection-based model reduction has become a popular approach to reduce the cost associated with integrating large-scale dynamical systems so they can be used in many-query settings such as optimization and uncertainty quantification. For…