Related papers: Optimization-Based Algebraic Multigrid Coarsening …

Divergence constraints are present in the governing equations of numerous physical phenomena, and they usually lead to a Poisson equation whose solution represents a bottleneck in many simulation codes. Algebraic Multigrid (AMG) is arguably…

Recovering sparse conditional independence graphs from data is a fundamental problem in machine learning with wide applications. A popular formulation of the problem is an $\ell_1$ regularized maximum likelihood estimation. Many convex…

This paper develops a new algebraic multigrid (AMG) method for sparse least-squares systems of the form $A=G^TG$ motivated by challenging applications in scientific computing where classical AMG methods fail. First we review and relate the…

Existing multi-agent coordination techniques are often fragile and vulnerable to anomalies such as agent attrition and communication disturbances, which are quite common in the real-world deployment of systems like field robotics. To better…

This paper studies Reinforcement Learning (RL) techniques to enable team coordination behaviors in graph environments with support actions among teammates to reduce the costs of traversing certain risky edges in a centralized manner. While…

Algebraic multigrid (AMG) is one of the fastest numerical methods for solving large sparse linear systems. For SPD matrices, convergence of AMG is well motivated in the $A$-norm, and AMG has proven to be an effective solver for many…

Graph Neural Networks (GNNs) have become powerful tools for learning from graph-structured data, finding applications across diverse domains. However, as graph sizes and connectivity increase, standard GNN training methods face significant…

The increasing share of renewable energy and distributed electricity generation requires the development of deep learning approaches to address the lack of flexibility inherent in traditional power grid methods. In this context, Graph…

Proper functioning of connected and automated vehicles (CAVs) is crucial for the safety and efficiency of future intelligent transport systems. Meanwhile, transitioning to fully autonomous driving requires a long period of mixed autonomy…

Stochastic optimization plays a crucial role in the advancement of deep learning technologies. Over the decades, significant effort has been dedicated to improving the training efficiency and robustness of deep neural networks, via various…

Algebraic multigrid (AMG) is an $\mathcal{O}(n)$ solution process for many large sparse linear systems. A hierarchy of progressively coarser grids is constructed that utilize complementary relaxation and interpolation operators. High-energy…

Partial Differential Equations (PDEs) underpin many scientific phenomena, yet traditional computational approaches often struggle with complex, nonlinear systems and irregular geometries. This paper introduces the AMG method, a Multi-Graph…

Graph Neural Networks (GNNs) have achieved state-of-the-art performance in solving graph classification tasks. However, most GNN architectures aggregate information from all nodes and edges in a graph, regardless of their relevance to the…

One main challenge in imbalanced graph classification is to learn expressive representations of the graphs in under-represented (minority) classes. Existing generic imbalanced learning methods, such as oversampling and imbalanced learning…

Laplacian matrices of graphs arise in large-scale computational applications such as machine learning; spectral clustering of images, genetic data and web pages; transportation network flows; electrical resistor circuits; and elliptic…

Graph Neural Networks (GNNs) are widely adopted in Web-related applications, serving as a core technique for learning from graph-structured data, such as text-attributed graphs. Yet in real-world scenarios, such graphs exhibit deficiencies…

Logic optimization is an NP-hard problem commonly approached through hand-engineered heuristics. We propose to combine graph convolutional networks with reinforcement learning and a novel, scalable node embedding method to learn which local…

This paper proposes a novel multi-agent reinforcement learning (MARL) method to learn multiple coordinated agents under directed acyclic graph (DAG) constraints. Unlike existing MARL approaches, our method explicitly exploits the DAG…

Recently, Graph Convolutional Networks (GCNs) have been widely studied for graph-structured data representation and learning. However, in many real applications, data are coming with multiple graphs, and it is non-trivial to adapt GCNs to…

In this paper, we develop a new parallel auxiliary grid algebraic multigrid (AMG) method to leverage the power of graphic processing units (GPUs). In the construction of the hierarchical coarse grid, we use a simple and fixed coarsening…