Model order reduction

Résumé

Model order reduction (MOR) is a technique for reducing the computational complexity of mathematical models in numerical simulations. As such it is closely related to the concept of metamodeling, with applications in all areas of mathematical modelling. Overview Many modern mathematical models of real-life processes pose challenges when used in numerical simulations, due to complexity and large size (dimension). Model order reduction aims to lower the computational complexity of such problems, for example, in simulations of large-scale dynamical systems and control systems. By a reduction of the model's associated state space dimension or degrees of freedom, an approximation to the original model is computed which is commonly referred to as a reduced order model. Reduced order models are useful in settings where it is often unfeasible to perform numerical simulations using the complete full order model. This can be due to limitations in computational resources or the requ

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https://en.wikipedia.org/wiki/Model_order_reduction

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Frequency-Domain Non-intrusive Greedy Model Order Reduction Based on Minimal Rational Approximation

Fabio Nobile, Davide Pradovera

We present a technique for Model Order Reduction (MOR) of frequency-domain problems relying on rational interpolation of vector-valued functions. The selection of the sample points is carried out adaptively according to a greedy procedure. We describe several options for the choice of a posteriori error indicators, which are used to drive the greedy algorithm and define its termination condition. Namely, we illustrate a tradeoff between each indicator's accuracy and its "intrusiveness", i.e. how much information on the underlying high-fidelity model needs to be available. We test numerically the effectiveness of this technique in solving a non-Hermitian eigen-problem and a microwave frequency response analysis.

SPRINGER INTERNATIONAL PUBLISHING AG2021

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During the past decade, model order reduction (MOR) has been successfully applied to reduce the computational complexity of elliptic and parabolic systems of partial differential equations (PDEs). However, MOR of hyperbolic equations remains a challenge. Symmetries and conservation laws, which are a distinctive feature of such systems, are often destroyed by conventional MOR techniques, resulting in a perturbed and often unstable reduced system. The goal of this thesis is to study and develop model order reduction techniques that can preserve nonlinear invariants, symmetries, and conservation laws and to understand the stability properties of these methods compared to conventional techniques. Hamiltonian systems, as systems that are driven by symmetries, are studied intensively from the point of view of MOR. Furthermore, a conservative model reduction of fluid flow is presented. It is illustrated that conserving invariants, conservation laws, and symmetries not only result in a physically meaningful reduced system but also result in an accurate and robust reduced system with enhanced stability.

EPFL2018

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We present a conceptually and computationally lightweight method for the design and iterative learning of fast maneuvers for quadrocopters. We use first-principles, reduced-order models and we do not require nor make an attempt to follow a specific state trajectory-only the initial and the final states of the vehicle are taken into account. We evaluate the adaptation scheme through experiments on quadrocopters in the ETH Flying Machine Arena that perform multi-flips and other high-performance maneuvers.

Springer Verlag2012

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