Related papers: Model order reduction of parametric dynamical syst…

Low-rank matrix completion (LRMC) problems arise in a wide variety of applications. Previous theory mainly provides conditions for completion under missing-at-random samplings. This paper studies deterministic conditions for completion. An…

Tensor completion is a fundamental tool for incomplete data analysis, where the goal is to predict missing entries from partial observations. However, existing methods often make the explicit or implicit assumption that the observed entries…

We introduce compositional tensor trains (CTTs) for the approximation of multivariate functions, a class of models obtained by composing low-rank functions in the tensor-train format. This format can encode standard approximation tools,…

A dynamic mode decomposition (DMD) based reduced-order model (ROM) is developed for tracking, detection, and prediction of kinetic plasma behavior. DMD is applied to the high-fidelity kinetic plasma model based on the electromagnetic…

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…

Reduced Order Modeling is of paramount importance for efficiently inferring high-dimensional spatio-temporal fields in parametric contexts, enabling computationally tractable parametric analyses, uncertainty quantification and control.…

A data-driven projection-based reduced-order model (ROM) for nonlinear thermal radiative transfer (TRT) problems is presented. The TRT ROM is formulated by (i) a hierarchy of low-order quasidiffusion (aka variable Eddington factor)…

Low-rank decomposition (LRD) is a state-of-the-art method for visual data reconstruction and modelling. However, it is a very challenging problem when the image data contains significant occlusion, noise, illumination variation, and…

We consider dynamical low-rank approximations to parabolic problems on higher-order tensor manifolds in Hilbert spaces. In addition to existence of solutions and their stability with respect to perturbations to the problem data, we show…

In this paper we propose novel methods for compression and recovery of multilinear data under limited sampling. We exploit the recently proposed tensor- Singular Value Decomposition (t-SVD)[1], which is a group theoretic framework for…

Even with the most advanced computational capabilities, high-fidelity (e.g., large-eddy) simulations of large-scale rocket engines remain far out of reach. In the current work, we develop and establish a component-based reduced-order…

We investigate the sensitivity of reduced order models (ROMs) to training data resolution as well as sampling rate. In particular, we consider proper orthogonal decomposition (POD), coupled with Galerkin projection (POD-GP), as an intrusive…

This paper surveys randomized algorithms in numerical linear algebra for low-rank decompositions of matrices and tensors. The survey begins with a review of classical matrix algorithms that can be accelerated by randomized dimensionality…

Decompositions of tensors into factor matrices, which interact through a core tensor, have found numerous applications in signal processing and machine learning. A more general tensor model which represents data as an ordered network of…

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…

We study low rank matrix and tensor completion and propose novel algorithms that employ adaptive sampling schemes to obtain strong performance guarantees. Our algorithms exploit adaptivity to identify entries that are highly informative for…

State estimation is key to both analyzing physical mechanisms and enabling real-time control of fluid flows. A common estimation approach is to relate sensor measurements to a reduced state governed by a reduced-order model (ROM). (When…

One of the popular approaches for low-rank tensor completion is to use the latent trace norm regularization. However, most existing works in this direction learn a sparse combination of tensors. In this work, we fill this gap by proposing a…

In this paper, we present a new adaptive rank approximation technique for computing solutions to the high-dimensional linear kinetic transport equation. The approach we propose is based on a macro-micro decomposition of the kinetic model in…

Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. These methods exploit the tensor structure of function spaces and apply…