Related papers: H2 Model Order Reduction: A Relative Error Setting
Projection-based model order reduction of dynamical systems usually introduces an error between the high-fidelity model and its counterpart of lower dimension. This unknown error can be bounded by residual-based methods, which are typically…
Model predictive controllers use dynamics models to solve constrained optimal control problems. However, computational requirements for real-time control have limited their use to systems with low-dimensional models. Nevertheless,…
Dynamical models described by ordinary differential equations (ODEs) are a fundamental tool in the sciences and engineering. Exact reduction aims at producing a lower-dimensional model in which each macro-variable can be directly related to…
Many complex engineering systems consist of multiple subsystems that are developed by different teams of engineers. To analyse, simulate and control such complex systems, accurate yet computationally efficient models are required. Modular…
A parametric model order reduction (MOR) approach for simulating the high dimensional models arising in financial risk analysis is proposed on the basis of the proper orthogonal decomposition (POD) approach to generate small model…
Model-order reduction techniques allow the construction of low-dimensional surrogate models that can accelerate engineering design processes. Often, these techniques are intrusive, meaning that they require direct access to underlying…
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…
The discretization of non-local operators, e.g., solution operators of partial differential equations or integral operators, leads to large densely populated matrices. $\mathcal{H}^2$-matrices take advantage of local low-rank structures in…
Relative error approaches are more of concern compared to absolute error ones such as the least square and least absolute deviation, when it needs scale invariant of output variable, for example with analyzing stock and survival data. An…
We introduce a model reduction approach for linear time-invariant second order systems based on positive real balanced truncation. Our method guarantees asymptotic stability and passivity of the reduced order model as well as the positive…
This paper presents an interpolatory framework for time-limited $H_2$ optimal model order reduction named Limited Time Iterative Rational Krylov Algorithm (LT-IRKA). The algorithm yields high fidelity reduced order models over limited time…
Advection-Diffusion-Reaction (ADR) Partial Differential Equations (PDEs) appear in a wide spectrum of applications such as chemical reactors, concentration flows, and biological systems. A large number of these applications require the…
Model order reduction (MOR) involves offering low-dimensional models that effectively approximate the behavior of complex high-order systems. Due to potential model complexities and computational costs, designing controllers for…
In this paper, a computationally efficient frequency-limited model reduction algorithm is presented for large-scale interconnected power systems. The algorithm generates a reduced order model which not only preserves the electromechanical…
In this paper, we establish a method for model order reduction of a certain class of physical network systems. The proposed method is based on clustering of the vertices of the underlying graph, and yields a reduced order model within the…
An adaptive parametric reduced-order modeling method based on interpolating poles of reduced-order models is proposed in this paper. To guarantee correct interpolation, a pole-matching process is conducted to determine which poles of two…
This paper investigates structure-preserving $H_2$-optimal model order reduction (MOR) for linear systems with quadratic outputs. Within a Petrov-Galerkin projection framework, the $H_2$-optimal MOR problem is first formulated as an…
In this work we present an extension of the technique of the order reduction to higher perturbative approximations in an iterative fashion. The intention is also to analyze more carefully the conditions for the validity of the order…
We present a data-driven framework for $h^{2}$-optimal model reduction for linear discrete-time systems. Our main contribution is to create optimal reduced-order models in the $h^{2}$-norm sense directly from the measurement data alone,…
Modern large-scale statistical models require to estimate thousands to millions of parameters. This is often accomplished by iterative algorithms such as gradient descent, projected gradient descent or their accelerated versions. What are…