Related papers: Graph Neural Preconditioners for Iterative Solutio…

Many artificial intelligence (AI) devices have been developed to accelerate the training and inference of neural networks models. The most common ones are the Graphics Processing Unit (GPU) and Tensor Processing Unit (TPU). They are highly…

Graph Neural Networks (GNNs) are widely used deep learning models that learn meaningful representations from graph-structured data. Due to the finite nature of the underlying recurrent structure, current GNN methods may struggle to capture…

Graph Neural Networks (GNNs) are a promising deep learning approach for circumventing many real-world problems on graph-structured data. However, these models usually have at least one of four fundamental limitations: over-smoothing,…

Iterative solvers preconditioned with algebraic multigrid have been devised as an optimal technology to speed up the response of large sparse linear systems. In this work, this technique was implemented in the framework of the dual…

This paper addresses the problem of scalable optimization for L1-regularized conditional Gaussian graphical models. Conditional Gaussian graphical models generalize the well-known Gaussian graphical models to conditional distributions to…

Linear programming (LP) is an extremely useful tool and has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…

Preconditioners are generally essential for fast convergence in the iterative solution of linear systems of equations. However, the computation of a good preconditioner can be expensive. So, while solving a sequence of many linear systems,…

We explore the use of graph neural networks (GNNs) to model spatial processes in which there is no a priori graphical structure. Similar to finite element analysis, we assign nodes of a GNN to spatial locations and use a computational…

Graph neural networks (GNNs) have been widely applied in multi-variate time-series forecasting (MTSF) tasks because of their capability in capturing the correlations among different time-series. These graph-based learning approaches improve…

The solution of linear systems of equations is a central task in a number of scientific and engineering applications. In many cases the solution of linear systems may take most of the simulation time thus representing a major bottleneck in…

Graph Neural Networks (GNNs) are widely used in many modern applications, necessitating explanations for their decisions. However, the complexity of GNNs makes it difficult to explain predictions. Even though several methods have been…

An implementation of GMRES with multiple preconditioners (MPGMRES) is proposed for solving shifted linear systems with shift-and-invert preconditioners. With this type of preconditioner, the Krylov subspace can be built without requiring…

Graph Neural Networks (GNNs) have become increasingly important due to their representational power and state-of-the-art predictive performance on many fundamental learning tasks. Despite this success, GNNs suffer from fairness issues that…

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…

Graph neural networks (GNNs) are a popular class of machine learning models whose major advantage is their ability to incorporate a sparse and discrete dependency structure between data points. Unfortunately, GNNs can only be used when such…

Neural Architecture Search (NAS) methods have shown to output networks that largely outperform human-designed networks. However, conventional NAS methods have mostly tackled the single dataset scenario, incuring in a large computational…

Despite recent progress in Graph Neural Networks (GNNs), explaining predictions made by GNNs remains a challenging open problem. The leading method independently addresses the local explanations (i.e., important subgraph structure and node…

We propose a geometry-aware strategy for training neural preconditioners tailored to parametrized linear systems arising from the discretization of mixed-dimensional partial differential equations (PDEs). These systems are typically…

We propose an end-to-end architecture for multivariate time-series prediction that integrates a spatial-temporal graph neural network with a matrix filtering module. This module generates filtered (inverse) correlation graphs from…

Least squares method is one of the simplest and most popular techniques applied in data fitting, imaging processing and high dimension data analysis. The classic methods like QR and SVD decomposition for solving least squares problems has a…