Related papers: Dynamical low-rank approximation for the semiclass…
We present a theoretical framework for equilibrium and nonequilibrium dynamical simulation of quantum states with spin-density-wave (SDW) order. Within a semiclassical adiabatic approximation that retains electron degrees of freedom, we…
This work studies the linear approximation of high-dimensional dynamical systems using low-rank dynamic mode decomposition (DMD). Searching this approximation in a data-driven approach is formalised as attempting to solve a low-rank…
In this study, we consider the numerical solution of large systems of linear equations obtained from the stochastic Galerkin formulation of stochastic partial differential equations. We propose an iterative algorithm that exploits the…
Semi-Definite Programming (SDP) with low-rank prior has been widely applied in Non-Rigid Structure from Motion (NRSfM). Based on a low-rank constraint, it avoids the inherent ambiguity of basis number selection in conventional base-shape or…
In this paper, we develop an efficient numerical solver for unsteady diffusion-type partial differential equations with random coefficients. A major computational challenge in such problems lies in repeatedly handling large-scale linear…
Dynamic Rank Reinforcement Learning (DR-RL) approximations rely on static rank assumptions, limiting their flexibility across diverse linguistic contexts. Our method dynamically modulates ranks based on real-time sequence dynamics,…
We propose a novel framework of generalised Petrov-Galerkin Dynamical Low Rank Approximations (DLR) in the context of random PDEs. It builds on the standard Dynamical Low Rank Approximations in their Dynamically Orthogonal formulation. It…
This paper addresses the stabilization of dynamical systems in the infinite horizon optimal control setting using nonlinear feedback control based on State-Dependent Riccati Equations (SDREs). While effective, the practical implementation…
In real-world applications, it is important for machine learning algorithms to be robust against data outliers or corruptions. In this paper, we focus on improving the robustness of a large class of learning algorithms that are formulated…
Randomness is ubiquitous in modern engineering. The uncertainty is often modeled as random coefficients in the differential equations that describe the underlying physics. In this work, we describe a two-step framework for numerically…
We propose a symmetric low-rank representation (SLRR) method for subspace clustering, which assumes that a data set is approximately drawn from the union of multiple subspaces. The proposed technique can reveal the membership of multiple…
The semiclassically scaled time-dependent multi-particle Schr\"odinger equation describes, inter alia, quantum dynamics of nuclei in a molecule. It poses the combined computational challenges of high oscillations and high dimensions. This…
Dynamic Mode Decomposition (DMD) has emerged as a powerful tool for analyzing the dynamics of non-linear systems from experimental datasets. Recently, several attempts have extended DMD to the context of low-rank approximations. This…
Efficient and accurate numerical approximation of the full Boltzmann equation has been a longstanding challenging problem in kinetic theory. This is mainly due to the high dimensionality of the problem and the complicated collision…
This paper introduces filtered finite difference methods for numerically solving a dispersive evolution equation with solutions that are highly oscillatory in both space and time. We consider a semiclassically scaled nonlinear Schr\"odinger…
We investigate discretizations of the integrable discrete nonlinear Schr\"odinger dynamical system and related symplectic structures. We develop an effective scheme of invariant reducing the corresponding infinite system of ordinary…
Low-rank plus diagonal (LRPD) decompositions provide a powerful structural model for large covariance matrices, simultaneously capturing global shared factors and localized corrections that arise in covariance estimation, factor analysis,…
In this paper, we propose a low-rank coordinate descent approach to structured semidefinite programming with diagonal constraints. The approach, which we call the Mixing method, is extremely simple to implement, has no free parameters, and…
This work develops a novel set of algorithms, alternating Gradient Descent (GD) and minimization for MRI (altGDmin-MRI1 and altGDmin-MRI2), for accelerated dynamic MRI by assuming an approximate low-rank (LR) model on the matrix formed by…
We introduce novel dynamical low-rank methods for solving large-scale matrix differential equations, motivated by algorithms from randomized numerical linear algebra. In terms of performance (cost and accuracy), our methods overperform…