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Estimating parameters of Partial Differential Equations (PDEs) is of interest in a number of applications such as geophysical and medical imaging. Parameter estimation is commonly phrased as a PDE-constrained optimization problem that can…
This paper proposes a data-driven algorithm for model order reduction (MOR) of large-scale wind farms and studies the effects that the obtained reduced-order model (ROM) has when this is integrated into the power grid. With respect to…
In this work, the dual-weighted residual (DWR) method is applied to obtain a certified incremental proper orthogonal decomposition (POD) based reduced order model. A novel approach called MORe DWR (Model Order Rduction with Dual-Weighted…
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…
We investigate the time domain model order reduction (MOR) framework using general orthogonal polynomials by Jiang and Chen 2012 and extend their idea by exploiting the structure of the corresponding linear system of equations. Identifying…
Reduced-order modeling (ROM) commonly refers to the construction, based on a few solutions (referred to as snapshots) of an expensive discretized partial differential equation (PDE), and the subsequent application of low-dimensional…
Solving optimal control problems for transport-dominated partial differential equations (PDEs) can become computationally expensive, especially when dealing with high-dimensional systems. To overcome this challenge, we focus on developing…
Scientific and engineering problems often involve parametric partial differential equations (PDEs), such as uncertainty quantification, optimizations, and inverse problems. However, solving these PDEs repeatedly can be prohibitively…
This work proposes a novel structure-preserving model order reduction (MOR) method for linear, time-invariant port-Hamiltonian (pH) systems. Our goal is to construct a reduced order pH system, which can still be interpreted in the physical…
The field of model order reduction (MOR) is growing in importance due to its ability to extract the key insights from complex simulations while discarding computationally burdensome and superfluous information. We provide an overview of MOR…
Most model reduction methods reduce the state dimension and then temporally evolve a set of coefficients that encode the state in the reduced representation. In this paper, we instead employ an efficient representation of the entire…
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…
We develop a novel deep learning technique, termed Deep Orthogonal Decomposition (DOD), for dimensionality reduction and reduced order modeling of parameter dependent partial differential equations. The approach consists in the construction…
In this paper, we propose an equation-based parametric Reduced Order Model (ROM), whose accuracy is improved with data-driven terms added into the reduced equations. These additions have the aim of reintroducing contributions that in…
Shape optimization is a challenging task in many engineering fields, since the numerical solutions of parametric system may be computationally expensive. This work presents a novel optimization procedure based on reduced order modeling,…
This contribution proposes novel data-driven surrogate modeling approaches for parameterized parabolic PDEs, where the parameter dependence can be split into two parts with different decay behavior of the Kolmogorov $N$-width. Such problems…
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…
Reduced basis methods are projection-based model order reduction techniques for reducing the computational complexity of solving parametrized partial differential equation problems. In this work we discuss the design of pyMOR, a freely…
In this work, we present a model order reduction technique for nonlinear structures assembled from components.The reduced order model is constructed by reducing the substructures with proper orthogonal decomposition and connecting them by a…
Nonlinear parametric inverse problems appear in several prominent applications; one such application is Diffuse Optical Tomography (DOT) in medical image reconstruction. Such inverse problems present huge computational challenges, mostly…