English
Related papers

Related papers: Accelerating Conjugate Gradient Solvers for Homoge…

200 papers

Solving large-scale linear systems problems is a cornerstone in scientific and industrial computing. Classical iterative solvers face increasing difficulty as the number of unknowns becomes large, while fully quantum linear solvers require…

Quantum Physics · Physics 2026-04-14 Shigetora Miyashita , Yoshi-aki Shimada

When simulating partial differential equations, hybrid solvers combine coarse numerical solvers with learned correctors. They promise accelerated simulations while adhering to physical constraints. However, as shown in our theoretical…

Machine Learning · Computer Science 2025-11-19 Hao Wei , Aleksandra Franz , Bjoern List , Nils Thuerey

The adoption of hybrid GPU-CPU nodes in traditional supercomputing platforms opens acceleration opportunities for electronic structure calculations in materials science and chemistry applications, where medium sized Hermitian generalized…

Numerical Analysis · Computer Science 2012-07-10 Raffaele Solcà , Thomas C. Schulthess , Azzam Haidar , Stanimire Tomov , Ichitaro Yamazaki , Jack Dongarra

This work presents UNO, a unified monocular visual odometry framework that enables robust and adaptable pose estimation across diverse environments, platforms, and motion patterns. Unlike traditional methods that rely on deployment-specific…

Computer Vision and Pattern Recognition · Computer Science 2025-06-10 Wentao Zhao , Yihe Niu , Yanbo Wang , Tianchen Deng , Shenghai Yuan , Zhenli Wang , Rui Guo , Jingchuan Wang

This paper presents a learnable solver tailored to iteratively solve sparse linear systems from discretized partial differential equations (PDEs). Unlike traditional approaches relying on specialized expertise, our solver streamlines the…

Numerical Analysis · Mathematics 2024-05-10 Yan Xie , Minrui Lv , Chensong Zhang

This work introduces a new approach for accelerating the numerical analysis of time-domain partial differential equations (PDEs) governing complex physical systems. The methodology is based on a combination of a classical reduced-order…

Machine Learning · Computer Science 2024-06-06 Victor Matray , Faisal Amlani , Frédéric Feyel , David Néron

We propose a new deflation strategy to accelerate the convergence of the preconditioned conjugate gradient(PCG) method for solving parametric large-scale linear systems of equations. Unlike traditional deflation techniques that rely on…

Numerical Analysis · Mathematics 2025-08-04 Alena Kopaničáková , Youngkyu Lee , George Em Karniadakis

Single-stage neural combinatorial optimization solvers have achieved near-optimal results on various small-scale combinatorial optimization (CO) problems without requiring expert knowledge. However, these solvers exhibit significant…

Artificial Intelligence · Computer Science 2025-01-22 Zhi Zheng , Changliang Zhou , Tong Xialiang , Mingxuan Yuan , Zhenkun Wang

Machine learning algorithms are becoming increasingly prevalent and performant in the reconstruction of events in accelerator-based neutrino experiments. These sophisticated algorithms can be computationally expensive. At the same time, the…

We present Unified PDE Solvers (UPS), a data- and compute-efficient approach to developing unified neural operators for diverse families of spatiotemporal PDEs from various domains, dimensions, and resolutions. UPS embeds different PDEs…

Machine Learning · Computer Science 2024-11-26 Junhong Shen , Tanya Marwah , Ameet Talwalkar

The numerical solution of partial differential equations (PDEs) is difficult, having led to a century of research so far. Recently, there have been pushes to build neural--numerical hybrid solvers, which piggy-backs the modern trend towards…

Machine Learning · Computer Science 2023-03-21 Johannes Brandstetter , Daniel Worrall , Max Welling

We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…

Machine Learning · Computer Science 2022-10-04 Ayano Kaneda , Osman Akar , Jingyu Chen , Victoria Kala , David Hyde , Joseph Teran

Natural Gradient Descent (NGD) has emerged as a promising optimization algorithm for training neural network-based solvers for partial differential equations (PDEs), such as Physics-Informed Neural Networks (PINNs). However, its practical…

Numerical Analysis · Mathematics 2026-05-28 Ivan Bioli , Carlo Marcati , Giancarlo Sangalli

Large linear systems are ubiquitous in modern computational science and engineering. The main recipe for solving them is the use of Krylov subspace iterative methods with well-designed preconditioners. Recently, GNNs have been shown to be a…

Machine Learning · Computer Science 2025-02-04 Vladislav Trifonov , Alexander Rudikov , Oleg Iliev , Yuri M. Laevsky , Ivan Oseledets , Ekaterina Muravleva

Linear solvers are key components in any software platform for scientific and engineering computing. The solution of large and sparse linear systems lies at the core of physics-driven numerical simulations relying on partial differential…

Numerical Analysis · Mathematics 2026-04-16 Massimo Bernaschi , Mauro G. Carrozzo , Alessandro Celestini , Giacomo Piperno , Pasqua D'Ambra

The optimization of multi-user multi-input multi-output (MU-MIMO) precoders is a widely recognized challenging problem. Existing work has demonstrated the potential of graph neural networks (GNNs) in learning precoding policies. However,…

Signal Processing · Electrical Eng. & Systems 2025-03-11 Lin Zhang , Shengqian Han , Chenyang Yang

We present a specific-purpose globalized and preconditioned Newton-CG solver to minimize a metric-aware curved high-order mesh distortion. The solver is specially devised to optimize curved high-order meshes for high polynomial degrees with…

Computational Engineering, Finance, and Science · Computer Science 2024-03-21 Guillermo Aparicio-Estrems , Abel Gargallo-Peiró , Xevi Roca

Neural-ODE parameterize a differential equation using continuous depth neural network and solve it using numerical ODE-integrator. These models offer a constant memory cost compared to models with discrete sequence of hidden layers in which…

Machine Learning · Computer Science 2025-03-27 Sheikh Waqas Akhtar

The observed and expected continued growth in the number of nodes in large-scale parallel computers gives rise to two major challenges: global communication operations are becoming major bottlenecks due to their limited scalability, and the…

Distributed, Parallel, and Cluster Computing · Computer Science 2020-02-03 Markus Levonyak , Christina Pacher , Wilfried N. Gansterer

Efficiently solving large-scale sparse linear systems poses a significant challenge in computational science, especially in fields such as physics, engineering, machine learning, and finance. Traditional classical algorithms face…

Quantum Physics · Physics 2024-10-04 Hakikat Singh