相关论文: Dynamical low-rank approximation for Burgers' equa…

Fine-tuning large-scale pre-trained models is inherently a resource-intensive task. While it can enhance the capabilities of the model, it also incurs substantial computational costs, posing challenges to the practical application of…

We propose a model reduction procedure for rapid and reliable solution of parameterized hyperbolic partial differential equations. Due to the presence of parameter-dependent shock waves and contact discontinuities, these problems are…

A multiscale numerical method is proposed for the solution of semi-linear elliptic stochastic partial differential equations with localized uncertainties and non-linearities, the uncertainties being modeled by a set of random parameters. It…

The simulation of many-body open quantum systems is key to solving numerous outstanding problems in physics, chemistry, material science, and in the development of quantum technologies. Near-term quantum computers may bring considerable…

We propose a numerical integrator for determining low-rank approximations to solutions of large-scale matrix differential equations. The considered differential equations are semilinear and stiff. Our method consists of first splitting the…

Over the past years Robust PCA has been established as a standard tool for reliable low-rank approximation of matrices in the presence of outliers. Recently, the Robust PCA approach via nuclear norm minimization has been extended to…

This article presents a fast solver for the dense "frontal" matrices that arise from the multifrontal sparse elimination process of 3D elliptic PDEs. The solver relies on the fact that these matrices can be efficiently represented as a…

We propose a new class of deep reinforcement learning (RL) algorithms that model latent representations in hyperbolic space. Sequential decision-making requires reasoning about the possible future consequences of current behavior.…

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…

An efficient technique based on low-rank separated approximations is proposed for computation of three-dimensional integrals arising in the energy deposition model that describes ion-atomic collisions. Direct tensor-product quadrature…

Dispersion of low-density rigid particles with complex geometries is ubiquitous in both natural and industrial environments. We show that while explicit methods for coupling the incompressible Navier-Stokes equations and Newton's equations…

In this paper, a mathematical formulation of the probabilistic available transfer capability (PATC) problem is proposed to incorporate uncertainties from the large-scale renewable energy generation (e.g., wind farms and solar PV power…

Binary optimization, a representative subclass of discrete optimization, plays an important role in mathematical optimization and has various applications in computer vision and machine learning. Usually, binary optimization problems are…

In this paper, we propose an innovative isogeometric low-rank solver for the linear elasticity model problem, specifically designed to allow multipatch domains. Our approach splits the domain into subdomains, each formed by the union of…

There are two primary approaches to solving Markov decision problems (MDPs): dynamic programming based on the Bellman equation and linear programming (LP). Dynamic programming methods are the most widely used and form the foundation of both…

Stochastic collocation (SC) is a well-known non-intrusive method of constructing surrogate models for uncertainty quantification. In dynamical systems, SC is especially suited for full-field uncertainty propagation that characterizes the…

We study the stability of a class of dynamical low-rank methods--the projector-splitting integrator (PSI)--applied to linear hyperbolic and parabolic equations. Using a von Neumann-type analysis, we investigate the stability of such…

In the Bayesian approach to inverse problems, data are often informative, relative to the prior, only on a low-dimensional subspace of the parameter space. Significant computational savings can be achieved by using this subspace to…

Algebraic Riccati equations with indefinite quadratic terms play an important role in applications related to robust controller design. While there are many established approaches to solve these in case of small-scale dense coefficients,…

In this work, we present an algorithmically tractable safe approximation of distributionally robust optimization (DRO) problems that contain univariate indicator functions. The latter appear in different applications, but render the model…