相关论文: A conservative low rank tensor method for the Vlas…

The goal of this paper is to find a low-rank approximation for a given tensor. Specifically, we give a computable strategy on calculating the rank of a given tensor, based on approximating the solution to an NP-hard problem. In this paper,…

Modern technological advances have enabled an unprecedented amount of structured data with complex temporal dependence, urging the need for new methods to efficiently model and forecast high-dimensional tensor-valued time series. This paper…

This paper presents the modal truncation and singular value decomposition (SVD) technique as two main algorithms for dynamic model reduction of the power system. The significance and accuracy of the proposed methods are investigated with…

Transformer architecture has gained popularity due to its ability to scale with large dataset. Consequently, there is a need to reduce the model size and latency, especially for on-device deployment. We focus on vision transformer proposed…

Tensor regression is an important tool for tensor data analysis, but existing works have not considered the impact of outliers, making them potentially sensitive to such data points. This paper proposes a low tubal rank robust regression…

In this paper, we consider a finite difference grid-based semi-Lagrangian approach in solving the Vlasov-Poisson (VP) system. Many of existing methods are based on dimensional splitting, which decouples the problem into solving linear…

This work studies the linear approximation of high-dimensional dynamical systems using low-rank dynamic mode decomposition (DMD). Searching this approximation in a data-driven approach is formalised as attempting to solve a low-rank…

We introduce and compare new compression approaches to obtain regularized solutions of large linear systems which are commonly encountered in large scale inverse problems. We first describe how to approximate matrix vector operations with a…

We propose an isogeometric solver for Poisson problems that combines i)low-rank tensor techniques to approximate the unknown solution and the system matrix, as a sum of a few terms having Kronecker product structure, ii) a Truncated…

We present a twofold contribution to the numerical simulation of Lindblad equations. First, an adaptive numerical approach to approximate Lindblad equations using low-rank dynamics is described: a deterministic low-rank approximation of the…

Computational methods for thermal radiative transfer problems exhibit high computational costs and a prohibitive memory footprint when the spatial and directional domains are finely resolved. A strategy to reduce such computational costs is…

We introduce the tensor numerical method for solving optimal control problems that are constrained by fractional 2D and 3D elliptic operators with variable coefficients. We solve the governing equation for the control function which…

In many applications such as data compression, imaging or genomic data analysis, it is important to approximate a given tensor by a tensor that is sparsely representable. For matrices, i.e. 2-tensors, such a representation can be obtained…

Recently, there has been a growing interest in efficient numerical algorithms based on tensor networks and low-rank techniques to approximate high-dimensional functions and solutions to high-dimensional PDEs. In this paper, we propose a new…

We propose a high order adaptive-rank implicit integrators for stiff time-dependent PDEs, leveraging extended Krylov subspaces to efficiently and adaptively populate low-rank solution bases. This allows for the accurate representation of…

Many problems encountered in plasma physics require a description by kinetic equations, which are posed in an up to six-dimensional phase space. A direct discretization of this phase space, often called the Eulerian approach, has many…

The widespread use of multisensor technology and the emergence of big datasets have created the need to develop tools to reduce, approximate, and classify large and multimodal data such as higher-order tensors. While early approaches…

Low rank tensor learning, such as tensor completion and multilinear multitask learning, has received much attention in recent years. In this paper, we propose higher order matching pursuit for low rank tensor learning problems with a convex…

Nonnegative Tucker decomposition (NTD) is a powerful tool for the extraction of nonnegative parts-based and physically meaningful latent components from high-dimensional tensor data while preserving the natural multilinear structure of…

Tensor decompositions have rich applications in statistics and machine learning, and developing efficient, accurate algorithms for the problem has received much attention recently. Here, we present a new method built on Kruskal's uniqueness…