相关论文: A high-order deterministic dynamical low-rank meth…

In this paper, we develop a low-rank method with high-order temporal accuracy using spectral deferred correction (SDC) to compute linear matrix differential equations. In [1], a low rank numerical method is proposed to correct the modeling…

Dynamical low-rank (DLR) approximation has gained interest in recent years as a viable solution to the curse of dimensionality in the numerical solution of kinetic equations including the Boltzmann and Vlasov equations. These methods…

Computing numerical solutions of the thermal radiative transfer equations on a finely resolved grid can be costly due to high computational and memory requirements. A numerical reduced order method that has recently been applied to a wide…

Direction of arrival (DOA) estimation is an important research in the area of array signal processing, and has been studied for decades. High resolution DOA estimation requires large array aperture, which leads to the increase of hardware…

We compute, from first principles, the absolute dose or fluence distribution per incident proton charge in a known heterogeneous terrain exposed to known proton beams. The algorithm is equally amenable to scattered or scanned beams. All…

We propose an inexact low-rank source iteration with diffusion synthetic acceleration (SI-DSA) for solving the multidimensional steady-state radiative transfer equation (RTE) in the second-order formulation. The angular flux is represented…

The low-rank matrix reconstruction (LRMR) approach is widely used in direction-of-arrival (DOA) estimation. As the rank norm penalty in an LRMR is NP-hard to compute, the nuclear norm (or the trace norm for a positive semidefinite (PSD)…

Nonlinear parametric inverse problems appear in many applications. Here, we focus on diffuse optical tomography (DOT) in medical imaging to recover unknown images of interest, such as cancerous tissue in a given medium, using a mathematical…

Treatment with high energy ionizing radiation is one of the main methods in modern cancer therapy that is in clinical use. During the last decades, two main approaches to dose calculation were used, Monte Carlo simulations and…

In this work, we propose an alternating low-rank decomposition (ALRD) approach and novel subspace algorithms for direction-of-arrival (DOA) estimation. In the ALRD scheme, the decomposition matrix for rank reduction is composed of a set of…

In this paper, we propose a dynamical low-rank (DLR) approximation framework for solving the semiclassical Schrodinger equation with uncertainties. The primary numerical challenges arise from the dual nature of the oscillations: the spatial…

In this paper, we introduce and analyze a new low-rank multilevel strategy for the solution of random diffusion problems. Using a standard stochastic collocation scheme, we first approximate the infinite dimensional random problem by a…

Compression has emerged as one of the essential deep learning research topics, especially for the edge devices that have limited computation power and storage capacity. Among the main compression techniques, low-rank compression via matrix…

Dynamical low-rank (DLR) approximation methods have previously been developed for time-dependent radiation transport problems. One crucial drawback of DLR is that it does not conserve important quantities of the calculation, which limits…

In this paper, we propose a new decomposition approach named the proximal primal dual algorithm (Prox-PDA) for smooth nonconvex linearly constrained optimization problems. The proposed approach is primal-dual based, where the primal step…

In this work, we design and analyze a Discrete de Rham (DDR) scheme for a contact mechanics problem involving fractures along which a model of Tresca friction is considered. Our approach is based on a mixed formulation involving a…

Dynamical low-rank algorithms are a class of numerical methods that compute low-rank approximations of dynamical systems. This is accomplished by projecting the dynamics onto a low-dimensional manifold and writing the solution directly in…

This work introduces reduced models based on Continuous Low Rank Adaptation (CoLoRA) that pre-train neural networks for a given partial differential equation and then continuously adapt low-rank weights in time to rapidly predict the…

Proton beam therapy has been developed to irradiate the tumor with higher precision and dose conformity compared to conventional X-ray irradiation. The dose conformity of this treatment modality may be further improved if narrower proton…

In this paper, we propose a low rank approximation method for efficiently solving stochastic partial differential equations. Specifically, our method utilizes a novel low rank approximation of the stiffness matrices, which can significantly…