Related papers: Optimization-Based Algebraic Multigrid Coarsening …

Implicit time integration is key to robustly simulating stiff materials and large deformations, but its performance is often dominated by repeatedly solving large linear systems. Adaptive coarsening can reduce this cost by concentrating…

The multigrid algorithm is an efficient numerical method for solving a variety of elliptic partial differential equations (PDEs). The method damps errors at progressively finer grid scales, resulting in faster convergence compared to…

This paper addresses matrix approximation problems for matrices that are large, sparse and/or that are representations of large graphs. To tackle these problems, we consider algorithms that are based primarily on coarsening techniques,…

Grouping problems aim to partition a set of items into multiple mutually disjoint subsets according to some specific criterion and constraints. Grouping problems cover a large class of important combinatorial optimization problems that are…

Graph convolutional networks (GCNs) have been employed as a kind of significant tool on many graph-based applications recently. Inspired by convolutional neural networks (CNNs), GCNs generate the embeddings of nodes by aggregating the…

We introduce a novel masked graph autoencoder (MGAE) framework to perform effective learning on graph structure data. Taking insights from self-supervised learning, we randomly mask a large proportion of edges and try to reconstruct these…

Combinatorial optimization problems are typically tackled by the branch-and-bound paradigm. We propose a new graph convolutional neural network model for learning branch-and-bound variable selection policies, which leverages the natural…

Deep Reinforcement Learning (DRL) has shown a dramatic improvement in decision-making and automated control problems. Consequently, DRL represents a promising technique to efficiently solve many relevant optimization problems (e.g.,…

Within the context of Graph Signal Processing (GSP), Graph Learning (GL) is concerned with the inference of the graph's underlying structure from nodal observations. However, real-world data often contains diverse information, necessitating…

Graph Visualization, also known as Graph Drawing, aims to find geometric embeddings of graphs that optimize certain criteria. Stress is a widely used metric; stress is minimized when every pair of nodes is positioned at their shortest path…

The excessive computational requirements of modern artificial neural networks (ANNs) are posing limitations on the machines that can run them. Sparsification of ANNs is often motivated by time, memory and energy savings only during model…

This paper proposes the method to optimize restriction and prolongation operators in the two-grid method. The proposed method is straightforwardly extended to the geometric multigrid method (GMM). GMM is used in solving discretized partial…

Graph Neural Networks (GNNs) have been popularly used for analyzing non-Euclidean data such as social network data and biological data. Despite their success, the design of graph neural networks requires a lot of manual work and domain…

Graph Neural Networks (GNNs) are a form of deep learning that enable a wide range of machine learning applications on graph-structured data. The learning of GNNs, however, is known to pose challenges for memory-constrained devices such as…

Adaptive mesh refinement (AMR) is necessary for efficient finite element simulations of complex physical phenomenon, as it allocates limited computational budget based on the need for higher or lower resolution, which varies over space and…

Graphical models capture relations between entities in a wide range of applications including social networks, biology, and natural language processing, among others. Graph neural networks (GNN) are neural models that operate over graphs,…

Combinatorial optimization problems are pervasive across science and industry. Modern deep learning tools are poised to solve these problems at unprecedented scales, but a unifying framework that incorporates insights from statistical…

Most compilers for machine learning (ML) frameworks need to solve many correlated optimization problems to generate efficient machine code. Current ML compilers rely on heuristics based algorithms to solve these optimization problems one at…

Graph Neural Networks (GNNs) have achieved remarkable success in graph-based learning by propagating information among neighbor nodes via predefined aggregation mechanisms. However, such fixed schemes often suffer from two key limitations.…

Graph Neural Networks (GNNs) have become the backbone for a myriad of tasks pertaining to graphs and similar topological data structures. While many works have been established in domains related to node and graph classification/regression…