Related papers: Graph Neural Preconditioners for Iterative Solutio…

Graph neural networks (GNNs) have proven their efficacy in a variety of real-world applications, but their underlying mechanisms remain a mystery. To address this challenge and enable reliable decision-making, many GNN explainers have been…

Graph neural networks (GNNs) have various practical applications, such as drug discovery, recommendation engines, and chip design. However, GNNs lack transparency as they cannot provide understandable explanations for their predictions. To…

The performance of sparse matrix computation highly depends on the matching of the matrix format with the underlying structure of the data being computed on. Different sparse matrix formats are suitable for different structures of data.…

Although some preconditioners are available for solving dense linear systems, there are still many matrices for which preconditioners are lacking, in particular in cases where the size of the matrix $N$ becomes very large. There remains…

Recently, message-passing graph neural networks (MPNNs) have shown potential for solving combinatorial and continuous optimization problems due to their ability to capture variable-constraint interactions. While existing approaches leverage…

Existing approaches to the crime prediction problem are unsuccessful in expressing the details since they assign the probability values to large regions. This paper introduces a new architecture with the graph convolutional networks (GCN)…

Predictive coding graphs (PCGs) are a recently introduced generalization to predictive coding networks, a neuroscience-inspired probabilistic latent variable model. Here, we prove how PCGs define a mathematical superset of feedforward…

Neural preconditioners for real-time physics simulation offer promising data-driven priors, but they often fail to capture long-range couplings efficiently because they inherit local message passing or sparse-operator access patterns. We…

Graph neural networks (GNNs) are popular to use for classifying structured data in the context of machine learning. But surprisingly, they are rarely applied to regression problems. In this work, we adopt GNN for a classic but challenging…

The challenge of effectively learning inter-series correlations for multivariate time series forecasting remains a substantial and unresolved problem. Traditional deep learning models, which are largely dependent on the Transformer paradigm…

Recommender system is one of the most important information services on today's Internet. Recently, graph neural networks have become the new state-of-the-art approach to recommender systems. In this survey, we conduct a comprehensive…

Graphs are ubiquitous for modeling complex relationships between objects across various fields. Graph neural networks (GNNs) have become a mainstream technique for graph-based applications, but their performance heavily relies on abundant…

Graph network-based simulators (GNS) have demonstrated strong potential for learning particle-based physics (such as fluids, deformable solids, and granular flows) while generalizing to unseen geometries due to their inherent inductive…

Graph processes model a number of important problems such as identifying the epicenter of an earthquake or predicting weather. In this paper, we propose a Graph Convolutional Recurrent Neural Network (GCRNN) architecture specifically…

Graph neural networks (GNNs) have pushed the state-of-the-art (SOTA) for performance in learning and predicting on large-scale data present in social networks, biology, etc. Since integrated circuits (ICs) can naturally be represented as…

Modeling multivariate time series has long been a subject that has attracted researchers from a diverse range of fields including economics, finance, and traffic. A basic assumption behind multivariate time series forecasting is that its…

Graph Neural Networks (GNNs) have emerged as a powerful tool to capture intricate network patterns, achieving success across different domains. However, existing GNNs require careful domain-specific architecture designs and training from…

Current simulation of metal forging processes use advanced finite element methods. Such methods consist of solving mathematical equations, which takes a significant amount of time for the simulation to complete. Computational time can be…

This paper introduces a new preconditioning technique that is suitable for matrices arising from the discretization of a system of PDEs on unstructured grids. The preconditioner satisfies a so-called filtering property, which ensures that…

This paper discusses parGeMSLR, a C++/MPI software library for the solution of sparse systems of linear algebraic equations via preconditioned Krylov subspace methods in distributed-memory computing environments. The preconditioner…