Related papers: The low-rank tensor-train finite difference method…
The low-rank approximation is a complexity reduction technique to approximate a tensor or a matrix with a reduced rank, which has been applied to the simulation of high dimensional problems to reduce the memory required and computational…
A linearized numerical scheme is proposed to solve the nonlinear time fractional parabolic problems with time delay. The scheme is based on the standard Galerkin finite element method in the spatial direction, the fractional Crank-Nicolson…
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…
Solving the Boltzmann-BGK equation with traditional numerical methods suffers from high computational and memory costs due to the curse of dimensionality. In this paper, we propose a novel accuracy-preserved tensor-train (APTT) method to…
We consider the task of low-multilinear-rank functional regression, i.e., learning a low-rank parametric representation of functions from scattered real-valued data. Our first contribution is the development and analysis of an efficient…
Higher-order low-rank tensors naturally arise in many applications including hyperspectral data recovery, video inpainting, seismic data recon- struction, and so on. We propose a new model to recover a low-rank tensor by simultaneously…
The problem of low-tubal-rank tensor estimation is a fundamental task with wide applications across high-dimensional signal processing, machine learning, and image science. Traditional approaches tackle such a problem by performing tensor…
This paper describes a flexible framework for generalized low-rank tensor estimation problems that includes many important instances arising from applications in computational imaging, genomics, and network analysis. The proposed estimator…
This paper is concerned with the development and analysis of an iterative solver for high-dimensional second-order elliptic problems based on subspace-based low-rank tensor formats. Both the subspaces giving rise to low-rank approximations…
Low-rank methods for kinetic equations have attracted increasing attention due to their effectiveness in reducing the high dimensionality of phase space. In our previous work [G. Wang & J. Hu, J. Comput. Phys. 558 (2026) 114884], we…
We introduce a family of numerical algorithms for the solution of linear system in higher dimensions with the matrix and right hand side given and the solution sought in the tensor train format. The proposed methods are rank--adaptive and…
Treating high dimensionality is one of the main challenges in the development of computational methods for solving problems arising in finance, where tasks such as pricing, calibration, and risk assessment need to be performed accurately…
Generalizing work of K\"unnemann, Paturi, and Schneider [ICALP 2017], we study a wide class of high-dimensional dynamic programming (DP) problems in which one must find the shortest path between two points in a high-dimensional grid given a…
Tensor completion is an extension of matrix completion aimed at recovering a multiway data tensor by leveraging a given subset of its entries (observations) and the pattern of observation. The low-rank assumption is key in establishing a…
In this paper, we introduce a tensor neural network based machine learning method for solving the elliptic partial differential equations with random coefficients in a bounded physical domain. With the help of tensor product structure, we…
Low rank matrix and tensor completion problems are to recover the incomplete two and higher order data by using their low rank structures. The essential problem in the matrix and tensor completion problems is how to improve the efficiency.…
Low-rank tensor approximation techniques attempt to mitigate the overwhelming complexity of linear algebra tasks arising from high-dimensional applications. In this work, we study the low-rank approximability of solutions to linear systems…
We present an efficient and robust numerical algorithm for solving the two-dimensional linear elasticity problem that combines the Quantized Tensor Train format and a domain partitioning strategy. This approach makes it possible to solve…
Tensor train (TT) decomposition provides a space-efficient representation for higher-order tensors. Despite its advantage, we face two crucial limitations when we apply the TT decomposition to machine learning problems: the lack of…
Multiway data often naturally occurs in a tensorial format which can be approximately represented by a low-rank tensor decomposition. This is useful because complexity can be significantly reduced and the treatment of large-scale data sets…