Related papers: Low-rank tensor product Richardson iteration for r…

The numerical solution of parameter identification inverse problems for kinetic equations can exhibit high computational and memory costs. In this paper, we propose a dynamical low-rank scheme for the reconstruction of the scattering…

We propose inexact subspace iteration for solving high-dimensional eigenvalue problems with low-rank structure. Inexactness stems from low-rank compression, enabling efficient representation of high-dimensional vectors in a low-rank tensor…

We consider the problem of low-rank decomposition of incomplete multiway tensors. Since many real-world data lie on an intrinsically low dimensional subspace, tensor low-rank decomposition with missing entries has applications in many data…

In three-dimensional (3D) radiative transfer (RT) problems, the tensor product quadratures are generally not optimal in terms of the number of discrete ray directions needed for a given accuracy of the angular integration of the radiation…

Rapid aerodynamic evaluation is crucial for modern vehicle design, yet existing neural operators struggle to capture intricate spatial correlations. We propose the rotary-enhanced transformer operator (RETO), a novel neural solver featuring…

This paper presents approximation methods for time-dependent thermal radiative transfer problems in high energy density physics. It is based on the multilevel quasidiffusion method defined by the high-order radiative transfer equation (RTE)…

A linear operator in a Hilbert space defined through the form of Riesz representation naturally introduces a reproducing kernel Hilbert space structure over the range space. Such formulation, called H-HK formulation in this paper, possesses…

Linear kinetic transport equations play a critical role in optical tomography, radiative transfer and neutron transport. The fundamental difficulty hampering their efficient and accurate numerical resolution lies in the high dimensionality…

Low-rank matrices are pervasive throughout statistics, machine learning, signal processing, optimization, and applied mathematics. In this paper, we propose a novel and user-friendly Euclidean representation framework for low-rank matrices.…

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…

Recent years have seen rapid advances in the data-driven analysis of dynamical systems based on Koopman operator theory and related approaches. On the other hand, low-rank tensor product approximations -- in particular the tensor train (TT)…

It is of great interest to solve the inverse problem of stationary radiative transport equation (RTE) in optical tomography. The standard way is to formulate the inverse problem into an optimization problem, but the bottleneck is that one…

This article presents an on-line tool (rttools.irap.omp.eu) and its accompanying software ressources for the numerical solution of basic radiation transfer out of local thermodynamic equilibrium (LTE). State-of-the-art stationary iterative…

Tensors with unit Frobenius norm are fundamental objects in many fields, including scientific computing and quantum physics, which are able to represent normalized eigenvectors and pure quantum states. While the tensor train decomposition…

Rotated reference frames offer fast algorithms for the radiative transport equation (RTE). We review the singular-eigenfunction approach and related numerical methods for the multi-dimensional RTE with rotated reference frames.

This paper studies the low-rank property of the inverse of a class of large-scale structured matrices in the tensor-train (TT) format, which is typically discretized from differential operators. An interesting question that we are concerned…

The problem of recovering a low $n$-rank tensor is an extension of sparse recovery problem from the low dimensional space (matrix space) to the high dimensional space (tensor space) and has many applications in computer vision and graphics…

We present a brief survey on the modern tensor numerical methods for multidimensional stationary and time-dependent partial differential equations (PDEs). The guiding principle of the tensor approach is the rank-structured separable…

We examine a method for solving an infinite-dimensional tensor eigenvalue problem $H x = \lambda x$, where the infinite-dimensional symmetric matrix $H$ exhibits a translational invariant structure. We provide a formulation of this type of…

The low-rank matrix recovery problem often arises in various fields, including signal processing, machine learning, and imaging science. The Riemannian gradient descent (RGD) algorithm has proven to be an efficient algorithm for solving…