Reduced Basis Methods: From Low-Rank Matrices To Low-Rank Tensors

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The detection of oxygen (O-2) by optical sensors is of growing importance, for example, in biology, life science, environmental science, and aerodynamics, where the composition of gases is crucial for many applications. Purely organic optical O-2 sensors a ...

This thesis focuses on the development and validation of a reduced order technique for cardiovascular simulations. The method is based on the combined use of the Reduced Basis method and a Domain Decomposition approach and can be seen as a particular imple ...

The Fourier-Galerkin method (in short FFTH) has gained popularity in numerical homogenisation because it can treat problems with a huge number of degrees of freedom. Because the method incorporates the fast Fourier transform (FFT) in the linear solver, it ...

Enabling analysis of non-linear systems in linear form, the Koopman operator has been shown to be a powerful tool for system identification and controller design. However, current data-driven methods cannot provide quantification of model uncertainty given ...

Many classical Computer Vision problems, such as essential matrix computation and pose estimation from 3D to 2D correspondences, can be tackled by solving a linear least-square problem, which can be done by finding the eigenvector corresponding to the smal ...

Matrices with hierarchical low-rank structure, including HODLR and HSS matrices, constitute a versatile tool to develop fast algorithms for addressing large-scale problems. While existing software packages for such matrices often focus on linear systems, t ...

We are interested in a reduced order method for the efficient simulation of blood flow in arteries. The blood dynamics is modeled by means of the incompressible Navier–Stokes equations. Our algorithm is based on an approximated domain-decomposition of the ...

Block Krylov subspace methods (KSMs) comprise building blocks in many state-of-the-art solvers for large-scale matrix equations as they arise, for example, from the discretization of partial differential equations. While extended and rational block Krylov ...

This article addresses the problem of simultaneous distributed state estimation, and control of linear systems with linear state feedback, subjected to process, and measurement noise, under the constraints of quantized, and rate-limited network data transm ...

We consider the finite-time stabilization of homogeneous quasilinear hyperbolic systems with one side controls and with nonlinear boundary condition at the other side. We present time-independent feedbacks leading to the finite-time stabilization in any ti ...

Many engineering fields rely on frequency-domain dynamical systems for the mathematical modeling of physical (electrical/mechanical/etc.) structures. With the growing need for more accurate and reliable results, the computational burden incurred by frequen ...

Long acquisition times preclude the application of multiecho spin echo (MESE) sequences for myelin water fraction (MWF) mapping in daily clinical practice. In search of alternative methods, previous studies of interest explored the biophysical modeling of ...

Reduced Basis Methods: From Low-Rank Matrices To Low-Rank Tensors

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Reversible and Broad-Range Oxygen Sensing Based on Purely Organic Long-Lived Photoemitters

Reduction techniques for PDEs built upon Reduced Basis and Domain Decomposition Methods with applications to hemodynamics

Energy-based comparison between the Fourier-Galerkin method and the finite element method

On Gaussian Process Based Koopman Operators

Eigendecomposition-Free Training of Deep Networks for Linear Least-Square Problems

hm-toolbox: MATLAB SOFTWARE FOR HODLR AND HSS MATRICES

Model order reduction of flow based on a modular geometrical approximation of blood vessels

Compress-and-restart block Krylov subspace methods for Sylvester matrix equations

A Distributed Luenberger Observer for Linear State Feedback Systems With Quantized and Rate-Limited Communications

Finite-time stabilization in optimal time of homogeneous quasilinear hyperbolic systems in one dimensional space

Model order reduction based on functional rational approximants for parametric PDEs with meromorphic structure

Data-driven myelin water imaging based on T-1 and T-2 relaxometry