Related papers: Multi-Level GNN Preconditioner for Solving Large S…

A primary computational problem in kernel regression is solution of a dense linear system with the $N\times N$ kernel matrix. Because a direct solution has an O($N^3$) cost, iterative Krylov methods are often used with fast matrix-vector…

Domain decomposition methods (DDMs) are popular solvers for discretized systems of partial differential equations (PDEs), with one-level and multilevel variants. These solvers rely on several algorithmic and mathematical parameters,…

In this paper, we present a data-driven approach to iteratively solve the discrete heterogeneous Helmholtz equation at high wavenumbers. In our approach, we combine classical iterative solvers with convolutional neural networks (CNNs) to…

The conjugate gradient solver (CG) is a prevalent method for solving symmetric and positive definite linear systems Ax=b, where effective preconditioners are crucial for fast convergence. Traditional preconditioners rely on prescribed…

Graph Convolutional Networks (GCNs) are extensively utilized for deep learning on graphs. The large data sizes of graphs and their vertex features make scalable training algorithms and distributed memory systems necessary. Since the…

Traditional clustering algorithms often struggle to capture the complex relationships within graphs and generalise to arbitrary clustering criteria. The emergence of graph neural networks (GNNs) as a powerful framework for learning…

Large Language Models (LLMs) have demonstrated strong reasoning abilities, making them suitable for complex tasks such as graph computation. Traditional reasoning steps paradigm for graph problems is hindered by unverifiable steps, limited…

Large-scale graph training is a notoriously challenging problem for graph neural networks (GNNs). Due to the nature of evolving graph structures into the training process, vanilla GNNs usually fail to scale up, limited by the GPU memory…

A recent Graph Neural Network (GNN) approach for learning to branch has been shown to successfully reduce the running time of branch-and-bound algorithms for Mixed Integer Linear Programming (MILP). While the GNN relies on a GPU for…

Mesh-based Graph Neural Networks (GNNs) have recently shown capabilities to simulate complex multiphysics problems with accelerated performance times. However, mesh-based GNNs require a large number of message-passing (MP) steps and suffer…

Graph neural networks (GNNs) are often trained on individual datasets, requiring specialized models and significant hyperparameter tuning due to the unique structures and features of each dataset. This approach limits the scalability and…

Graph Neural Networks (GNNs) are powerful tools for learning graph-structured data, but their scalability is hindered by inefficient mini-batch generation, data transfer bottlenecks, and costly inter-GPU synchronization. Existing training…

Graph Neural Networks (GNNs) are deep-learning architectures designed for graph-type data, where understanding relationships among individual observations is crucial. However, achieving promising GNN performance, especially on unseen data,…

Graph Neural Networks (GNNs) are powerful deep learning models to generate node embeddings on graphs. When applying deep GNNs on large graphs, it is still challenging to perform training in an efficient and scalable way. We propose a novel…

Neural networks often struggle with high-dimensional but small sample-size tabular datasets. One reason is that current weight initialisation methods assume independence between weights, which can be problematic when there are insufficient…

Continuum mechanics simulators, numerically solving one or more partial differential equations, are essential tools in many areas of science and engineering, but their performance often limits application in practice. Recent modern machine…

While Annealing Machines (AM) have shown increasing capabilities in solving complex combinatorial problems, positioning themselves as a more immediate alternative to the expected advances of future fully quantum solutions, there are still…

Full batch training of Graph Convolutional Network (GCN) models is not feasible on a single GPU for large graphs containing tens of millions of vertices or more. Recent work has shown that, for the graphs used in the machine learning…

This work develops a distributed graph neural network (GNN) methodology for mesh-based modeling applications using a consistent neural message passing layer. As the name implies, the focus is on enabling scalable operations that satisfy…

Rule-based fine-grained IP geolocation methods are hard to generalize in computer networks which do not follow hypothetical rules. Recently, deep learning methods, like multi-layer perceptron (MLP), are tried to increase generalization…