Related papers: Faster Local Solvers for Graph Diffusion Equations

Generative models such as Generative Adversarial Networks (GANs) and Variational Auto-Encoders (VAEs) are widely utilized to model the generative process of user interactions. However, these generative models suffer from intrinsic…

A local weighted discontinuous Galerkin gradient discretization method for solving elliptic equations is introduced. The local scheme is based on a coarse grid and successively improves the solution solving a sequence of local elliptic…

Learning to generate graphs is challenging as a graph is a set of pairwise connected, unordered nodes encoding complex combinatorial structures. Recently, several works have proposed graph generative models based on normalizing flows or…

Graph neural network (GNN) is a promising approach to learning and predicting physical phenomena described in boundary value problems, such as partial differential equations (PDEs) with boundary conditions. However, existing models…

Graph Neural Networks (GNNs) are important across different domains, such as social network analysis and recommendation systems, due to their ability to model complex relational data. This paper introduces subgraph queries as a new task for…

While many systems have been developed to train Graph Neural Networks (GNNs), efficient model inference and evaluation remain to be addressed. For instance, using the widely adopted node-wise approach, model evaluation can account for up to…

In network analysis and graph mining, closeness centrality is a popular measure to infer the importance of a vertex. Computing closeness efficiently for individual vertices received considerable attention. The NP-hard problem of group…

Network-based Global Navigation Satellite Systems (GNSS) underpin critical infrastructure and autonomous systems, yet typically rely on centralized processing hubs that limit scalability, resilience, and latency. Here we report a…

Graph diffusion models have recently been proposed to synthesize entire graphs, such as molecule graphs. Although existing methods have shown great performance in generating entire graphs for graph-level learning tasks, no graph diffusion…

High parallel framework has been proved to be very suitable for graph processing. There are various work to optimize the implementation in FPGAs, a pipeline parallel device. The key to make use of the parallel performance of FPGAs is to…

This paper considers the existence of local and global-in-time strong solutions to the advection-diffusion equation with variable coefficients on an evolving surface with a boundary. We apply both the maximal $L^p$-in-time regularity for…

Dynamic Graph Neural Network (DGNN) has shown a strong capability of learning dynamic graphs by exploiting both spatial and temporal features. Although DGNN has recently received considerable attention by AI community and various DGNN…

Diffusion models have recently been recognised as efficient inverse problem solvers due to their ability to produce high-quality reconstruction results without relying on pairwise data training. Existing diffusion-based solvers utilize…

Diffusion kernels over graphs have been widely utilized as effective tools in various applications due to their ability to accurately model the flow of information through nodes and edges. However, there is a notable gap in the literature…

Memory-based Temporal Graph Neural Networks are powerful tools in dynamic graph representation learning and have demonstrated superior performance in many real-world applications. However, their node memory favors smaller batch sizes to…

Coarse graining is an important ingredient in many multi-scale continuum-discrete solvers such as CFD--DEM (computational fluid dynamics--discrete element method) solvers for dense particle-laden flows. Although CFD--DEM solvers have become…

Recent research has made significant progress in optimizing diffusion models for downstream objectives, which is an important pursuit in fields such as graph generation for drug design. However, directly applying these models to graph…

Graph classification is a challenging problem owing to the difficulty in quantifying the similarity between graphs or representing graphs as vectors, though there have been a few methods using graph kernels or graph neural networks (GNNs).…

This paper considers the problem of resource allocation in stream processing, where continuous data flows must be processed in real time in a large distributed system. To maximize system throughput, the resource allocation strategy that…

Graph neural networks (GNNs) have demonstrated excellent performance in a wide range of applications. However, the enormous size of large-scale graphs hinders their applications under real-time inference scenarios. Although existing…