Related papers: Model Reduction for Switched Linear Systems via Ge…
In many areas of engineering, nonlinear numerical analysis is playing an increasingly important role in supporting the design and monitoring of structures. Whilst increasing computer resources have made such formerly prohibitive analyses…
Regressions created from experimental or simulated data enable the construction of metamodels, widely used in a variety of engineering applications. Many engineering problems involve multi-parametric physics whose corresponding…
Nonlinear balanced truncation is a model order reduction technique that reduces the dimension of nonlinear systems in a manner that accounts for either open- or closed-loop observability and controllability aspects of the system. Two…
In this paper, we present a projection-based model-order reduction (MOR) technique for smoothed particle hydrodynamics (SPH) simulations, which is a mesh-free approach within the Lagrangian framework. Our approach utilizes the proper…
A methodology grounded in model reduction is presented for accelerating the gradient-based solution of a family of linear or nonlinear constrained optimization problems where the constraints include at least one linear Partial Differential…
In this paper, we present a theoretical analysis of the model reduction algorithm for linear switched systems. This algorithm is a reminiscence of the balanced truncation method for linear parameter varying systems. Specifically in this…
Recent works have shown that imposing tensor structures on the coefficient tensor in regression problems can lead to more reliable parameter estimation and lower sample complexity compared to vector-based methods. This work investigates a…
The Zwanzig-Mori pro jection formalism is widely used in studying systems with many degrees of freedom. Recently Xing and Kim used the pro jection formalism and derived the generalized Langevin equations (GLEs) for a general stochastic…
Finite element based simulation of phenomena governed by partial differential equations is a standard tool in many engineering workflows today. However, the simulation of complex geometries is computationally expensive. Many engineering…
This paper proposes lower bounds on a quantity called $L^p$-norm joint spectral radius, or in short, $p$-radius, of a finite set of matrices. Despite its wide range of applications to, for example, stability analysis of switched linear…
We describe a parallel iterative least squares solver named \texttt{LSRN} that is based on random normal projection. \texttt{LSRN} computes the min-length solution to $\min_{x \in \mathbb{R}^n} \|A x - b\|_2$, where $A \in \mathbb{R}^{m…
The paper presents a Projection-Based Reduced-Order Model for simulations of high Reynolds turbulent flows. The PBROM are enhanced by incorporating various models of turbulent viscosity and residual closures to model the effects of…
Purpose: We address the challenge of inaccurate parameter estimation in diffusion MRI when the signal-to-noise ratio (SNR) is very low, as in the spinal cord. The accuracy of conventional maximum-likelihood estimation (MLE) depends highly…
In this paper, we investigate the use of multilinear algebra for reducing the order of multidimensional linear time-invariant (MLTI) systems. Our main tools are tensor rational Krylov subspace methods, which enable us to approximate the…
Pruning is widely recognized as an effective method for reducing the parameters of large language models (LLMs), potentially leading to more efficient deployment and inference. One classic and prominent path of LLM one-shot pruning is to…
An iterative method LSMR is presented for solving linear systems $Ax=b$ and least-squares problem $\min \norm{Ax-b}_2$, with $A$ being sparse or a fast linear operator. LSMR is based on the Golub-Kahan bidiagonalization process. It is…
This paper tackles state feedback control of switched linear systems under arbitrary switching. We propose a data-driven control framework that allows to compute a stabilizing state feedback using only a finite set of observations of…
Model order reduction (MOR) techniques play a crucial role in the computer-aided design of modern integrated circuits, where they are used to reduce the size of parasitic networks. Unfortunately, the efficient reduction of passive networks…
Sparse linear regression, which entails finding a sparse solution to an underdetermined system of linear equations, can formally be expressed as an $l_0$-constrained least-squares problem. The Orthogonal Least-Squares (OLS) algorithm…
This paper presents a model order reduction (MOR) approach for high dimensional problems in the analysis of financial risk. To understand the financial risks and possible outcomes, we have to perform several thousand simulations of the…