Related papers: A high-order deterministic dynamical low-rank meth…

Protein inverse folding is a fundamental problem in bioinformatics, aiming to recover the amino acid sequences from a given protein backbone structure. Despite the success of existing methods, they struggle to fully capture the intricate…

We propose a parallel algorithm for the numerical solution of a class of second order semi-linear equations coming from stochastic optimal control problems, by means of a dynamic domain decomposition technique. The new method is an…

We propose a dynamical low-rank algorithm for a gyrokinetic model that is used to describe strongly magnetized plasmas. The low-rank approximation is based on a decomposition into variables parallel and perpendicular to the magnetic field,…

We develop new dynamically orthogonal tensor methods to approximate multivariate functions and the solution of high-dimensional time-dependent nonlinear partial differential equations (PDEs). The key idea relies on a hierarchical…

Low-rank gradient compression reduces communication in distributed training by representing updates with rank-$r$ factors. Dion is a recent method that approximates Muon, a spectral optimizer that orthogonalizes momentum, using one step of…

This paper proposes a new framework for computing low-rank solutions to nonlinear matrix equations arising from spatial discretization of nonlinear partial differential equations: low-rank Anderson acceleration (lrAA). lrAA is an adaptation…

Low-rank decomposition (LRD) is a state-of-the-art method for visual data reconstruction and modelling. However, it is a very challenging problem when the image data contains significant occlusion, noise, illumination variation, and…

We introduce a new discrete-ordinate scheme for solving the general relativistic Boltzmann transport equation in the context of core-collapse supernovae. Our algorithm avoids the need to spell out the complicated advection terms in energy…

Many studies have been conducted to improve the efficiency of Transformer from quadric to linear. Among them, the low-rank-based methods aim to learn the projection matrices to compress the sequence length. However, the projection matrices…

With the ever-growing size of pretrained models (PMs), fine-tuning them has become more expensive and resource-hungry. As a remedy, low-rank adapters (LoRA) keep the main pretrained weights of the model frozen and just introduce some…

In this manuscript, we research on the behaviors of surrogates for the rank function on different image processing problems and their optimization algorithms. We first propose a novel nonconvex rank surrogate on the general rank…

A new domain decomposition method is introduced for the heterogeneous 2-D and 3-D Helmholtz equations. Transmission conditions based on the perfectly matched layer (PML) are derived that avoid artificial reflections and match incoming and…

Solving high-dimensional parabolic partial differential equations (PDEs) with deep learning methods is often computationally and memory intensive, primarily due to the need for automatic differentiation (AD) to compute large Hessian…

Deep reinforcement learning (DRL) has achieved remarkable progress in online path planning tasks for multi-UAV systems. However, existing DRL-based methods often suffer from performance degradation when tackling unseen scenarios, since the…

Low-rank adaptation (LoRA) is a parameter-efficient fine-tuning (PEFT) method widely used in large language models (LLMs). LoRA essentially describes the projection of an input space into a low-dimensional output space, with the…

Deep learning models in satellite onboard enable real-time interpretation of remote sensing images, reducing the need for data transmission to the ground and conserving communication resources. As satellite numbers and observation…

We present a preconditioned Monte Carlo method for computing high-dimensional multivariate normal and Student-$t$ probabilities arising in spatial statistics. The approach combines a tile-low-rank representation of covariance matrices with…

Laser-accelerated protons have a great potential for innovative experiments in radiation biology due to the sub-picosecond pulse duration and high dose rate achievable. However, the broad angular divergence makes them not optimal for…

We present a novel method called TESALOCS (TEnsor SAmpling and LOCal Search) for multidimensional optimization, combining the strengths of gradient-free discrete methods and gradient-based approaches. The discrete optimization in our method…

Low-rank representation (LRR) is an effective method for subspace clustering and has found wide applications in computer vision and machine learning. The existing LRR solver is based on the alternating direction method (ADM). It suffers…