Related papers: A robust and conservative dynamical low-rank algor…
In this paper, we propose a novel adaptive-rank method for simulating multi-scale BGK equations, based on a greedy sampling strategy. The method adaptively selects important rows and columns of the solution matrix and updates them using a…
The performance of Deep Neural Networks (DNNs) keeps elevating in recent years with increasing network depth and width. To enable DNNs on edge devices like mobile phones, researchers proposed several network compression methods including…
The dynamical low-rank (DLR) approximation is an efficient technique to approximate the solution to matrix differential equations. Recently, the DLR method was applied to radiation transport calculations to reduce memory requirements and…
Radiation transport problems are posed in a high-dimensional phase space, limiting the use of finely resolved numerical simulations. An emerging tool to efficiently reduce computational costs and memory footprint in such settings is…
This paper presents a weakly intrusive strategy for computing a low-rank approximation of the solution of a system of nonlinear parameter-dependent equations. The proposed strategy relies on a Newton-like iterative solver which only…
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…
Approximations of functions with finite data often do not respect certain "structural" properties of the functions. For example, if a given function is non-negative, a polynomial approximation of the function is not necessarily also…
This paper is devoted to proposing a general weighted low-rank recovery model and designing a fast SVD-free computational scheme to solve it. First, our generic weighted low-rank recovery model unifies several existing approaches in the…
Inference and simulation in the context of high-dimensional dynamical systems remain computationally challenging problems. Some form of dimensionality reduction is required to make the problem tractable in general. In this paper, we propose…
Robust low-rank matrix completion (RMC), or robust principal component analysis with partially observed data, has been studied extensively for computer vision, signal processing and machine learning applications. This problem aims to…
Low-rank approximation of a matrix by means of structured random sampling has been consistently efficient in its extensive empirical studies around the globe, but adequate formal support for this empirical phenomenon has been missing so…
In this paper, we present an efficient method for storing fine-tuned models by leveraging the low-rank properties of weight residuals. Our key observation is that weight residuals in large overparameterized models exhibit even stronger…
To enable DNNs on edge devices like mobile phones, low-rank approximation has been widely adopted because of its solid theoretical rationale and efficient implementations. Several previous works attempted to directly approximate a…
Unlike the matrix case, computing low-rank approximations of tensors is NP-hard and numerically ill-posed in general. Even the best rank-1 approximation of a tensor is NP-hard. In this paper, we use convex optimization to develop…
The Vlasov--Maxwell equations are used for the kinetic description of magnetized plasmas. As they are posed in an up to 3+3 dimensional phase space, solving this problem is extremely expensive from a computational point of view. In this…
The dynamical low-rank approximation (DLRA) is used to treat high-dimensional problems that arise in such diverse fields as kinetic transport and uncertainty quantification. Even though it is well known that certain spatial and temporal…
We develop two new sets of stable, rank-adaptive Dynamically Orthogonal Runge-Kutta (DORK) schemes that capture the high-order curvature of the nonlinear low-rank manifold. The DORK schemes asymptotically approximate the truncated singular…
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…
Low-rank modeling has a lot of important applications in machine learning, computer vision and social network analysis. While the matrix rank is often approximated by the convex nuclear norm, the use of nonconvex low-rank regularizers has…
In this paper, we propose a new algorithm for recovery of low-rank matrices from compressed linear measurements. The underlying idea of this algorithm is to closely approximate the rank function with a smooth function of singular values,…