Related papers: Certified Model Order Reduction for parametric Her…
In order to investigate correspondences between 3D shapes, many methods rely on a feature descriptor which is invariant under almost isometric transformations. An interesting class of models for such descriptors relies on partial…
A novel method for performing model updating on finite element models is presented. The approach is particularly tailored to modal analyses of buildings, by which the lowest frequencies, obtained by using sensors and system identification…
This paper investigates the optimal $H_2$ model order reduction for linear systems with quadratic outputs. In the framework of Galerkin projection, we first formulate the optimal $H_2$ MOR as an unconstrained Riemannian optimization problem…
A ubiquitous challenge in design space exploration or uncertainty quantification of complex engineering problems is the minimization of computational cost. A useful tool to ease the burden of solving such systems is model reduction. This…
A non-intrusive model order reduction (MOR) method for solving parameterized electromagnetic scattering problems is proposed in this paper. A database collecting snapshots of high-fidelity solutions is built by solving the parameterized…
Assume that the eigenvalues of a finite hermitian linear operator have been deduced accurately but the linear operator itself could not be determined with precision. Given a set of eigenvalues $\lambda$ and a hermitian matrix $M$, this…
This paper studies the problem of selecting a submatrix of a positive definite matrix in order to achieve a desired bound on the smallest eigenvalue of the submatrix. Maximizing this smallest eigenvalue has applications to selecting input…
In this work, we propose to efficiently solve time dependent parametrized optimal control problems governed by parabolic partial differential equations through the certified reduced basis method. In particular, we will exploit an error…
We introduce a framework for repurposing error estimators for source problems to compute an estimator for the gap between eigenspaces and their discretizations. Of interest are eigenspaces of finite clusters of eigenvalues of unbounded…
In this document, some elements of the theory and algorithmics corresponding to the existence and computability of approximate joint eigenpairs for finite collections of matrices with applications to model order reduction, are presented.…
Quantum subspace diagonalization methods are an exciting new class of algorithms for solving large\rev{-}scale eigenvalue problems using quantum computers. Unfortunately, these methods require the solution of an ill-conditioned generalized…
We present a new method for computing the lowest few eigenvalues and the corresponding eigenvectors of a nuclear many-body Hamiltonian represented in a truncated configuration interaction subspace, i.e., the no-core shell model (NCSM). The…
We propose and study an algorithm for computing a nearest passive system to a given non-passive linear time-invariant system (with much freedom in the choice of the metric defining `nearest', which may be restricted to structured…
In this work, we consider the matrix completion problem, where the objective is to reconstruct a low-rank matrix from a few observed entries. A commonly employed approach involves nuclear norm minimization. For this method to succeed, the…
Meaningful comparison between sets of observations often necessitates alignment or registration between them, and the resulting optimization problems range in complexity from those admitting simple closed-form solutions to those requiring…
Numerical simulations are crucial for comprehending how engineering structures behave under extreme conditions, particularly when dealing with thermo-mechanically coupled issues compounded by damage-induced material softening. However, such…
For many applications in signal processing and machine learning, we are tasked with minimizing a large sum of convex functions subject to a large number of convex constraints. In this paper, we devise a new random projection method (RPM) to…
Model order reduction (MOR) is crucial for the design process of integrated circuits. Specifically, the vast amount of passive RLCk elements in electromagnetic models extracted from physical layouts exacerbates the extraction time, the…
Parameter prediction is essential for many applications, facilitating insightful interpretation and decision-making. However, in many real life domains, such as power systems, medicine, and engineering, it can be very expensive to acquire…
An adaptive projection-based reduced-order model (ROM) formulation is presented for model-order reduction of problems featuring chaotic and convection-dominant physics. An efficient method is formulated to adapt the basis at every time-step…