Related papers: Randomized methods for dynamical low-rank approxim…
We study efficient solution methods for stochastic eigenvalue problems arising from discretization of self-adjoint partial differential equations with random data. With the stochastic Galerkin approach, the solutions are represented as…
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…
In this paper, we propose a novel Local Macroscopic Conservative (LoMaC) low rank tensor method with discontinuous Galerkin (DG) discretization for the physical and phase spaces for simulating the Vlasov-Poisson (VP) system. The LoMaC…
Matrix decompositions are fundamental tools in the area of applied mathematics, statistical computing, and machine learning. In particular, low-rank matrix decompositions are vital, and widely used for data analysis, dimensionality…
In the present paper, we consider large-scale differential Lyapunov matrix equations having a low rank constant term. We present two new approaches for the numerical resolution of such differential matrix equations. The first approach is…
We propose a low-rank tensor approach to approximate linear transport and nonlinear Vlasov solutions and their associated flow maps. The approach takes advantage of the fact that the differential operators in the Vlasov equation is tensor…
In this paper, we present a Rank Revealing Randomized Singular Value Decomposition (R3SVD) algorithm to incrementally construct a low-rank approximation of a potentially large matrix while adaptively estimating the appropriate rank that can…
We consider chance-constrained problems with discrete random distribution. We aim for problems with a large number of scenarios. We propose a novel method based on the stochastic gradient descent method which performs updates of the…
In this work (Part I), we study three time-discretization procedures of the Dynamical Low-Rank Approximation (DLRA) of high-dimensional stochastic differential equations (SDEs). Specifically, we consider the Dynamically Orthogonal (DO)…
This paper tackles the challenge of parameter calibration in stochastic models, particularly in scenarios where the likelihood function is unavailable in an analytical form. We introduce a gradient-based simulated parameter estimation…
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…
Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. These methods exploit the tensor structure of function spaces and apply…
The Nystr\"om method is a popular choice for finding a low-rank approximation to a symmetric positive semi-definite matrix. The method can fail when applied to symmetric indefinite matrices, for which the error can be unboundedly large. In…
Many applications in data science and scientific computing involve large-scale datasets that are expensive to store and compute with, but can be efficiently compressed and stored in an appropriate tensor format. In recent years, randomized…
We study the problem of estimating low-rank matrices from linear measurements (a.k.a., matrix sensing) through nonconvex optimization. We propose an efficient stochastic variance reduced gradient descent algorithm to solve a nonconvex…
Recent developments in engineering techniques for spatial data collection such as geographic information systems have resulted in an increasing need for methods to analyze large spatial data sets. These sorts of data sets can be found in…
We propose a new randomized algorithm for solving convex optimization problems that have a large number of constraints (with high probability). Existing methods like interior-point or Newton-type algorithms are hard to apply to such…
The Nystr\"om method offers an effective way to obtain low-rank approximation of SPD matrices, and has been recently extended and analyzed to nonsymmetric matrices (leading to the generalized Nystr\"om method). It is a randomized,…
Randomized algorithms provide solutions to two ubiquitous problems: (1) the distributed calculation of a principal component analysis or singular value decomposition of a highly rectangular matrix, and (2) the distributed calculation of a…
Recent work has suggested using Monte Carlo methods based on piecewise deterministic Markov processes (PDMPs) to sample from target distributions of interest. PDMPs are non-reversible continuous-time processes endowed with momentum, and…