相关论文: Faster Local Solvers for Graph Diffusion Equations

We present a GPU-accelerated version of a high-order discontinuous Galerkin discretization of the unsteady incompressible Navier-Stokes equations. The equations are discretized in time using a semi-implicit scheme with explicit treatment of…

The analogy to heat diffusion has enhanced our understanding of information flow in graphs and inspired the development of Graph Neural Networks (GNNs). However, most diffusion-based GNNs emulate passive heat diffusion, which still suffers…

Graph neural networks (GNNs) are powerful tools for exploring and learning from graph structures and features. As such, achieving high-performance execution for GNNs becomes crucially important. Prior works have proposed to explore the…

Graph neural networks (GNNs), especially dynamic GNNs, have become a research hotspot in spatio-temporal forecasting problems. While many dynamic graph construction methods have been developed, relatively few of them explore the causal…

At present, deep learning based methods are being employed to resolve the computational challenges of high-dimensional partial differential equations (PDEs). But the computation of the high order derivatives of neural networks is costly,…

City-scale logistics routing has become increasingly challenging as metropolitan road networks grow to tens of millions of edges and traffic conditions evolve rapidly under high-volume mobility demands. Conventional centralized routing…

In this paper, we propose the first framework that enables solving graph learning tasks of all levels (node, edge and graph) and all types (generation, regression and classification) using one formulation. We first formulate prediction…

Normal and anomalous diffusion are ubiquitous in many complex systems [1] . Here, we define a time and space generalized diffusion equation (GDE), which uses fractional-time derivatives and transformed d-path Laplacian operators on…

In this paper, we propose an efficient high order semi-Lagrangian (SL) discontinuous Galerkin (DG) method for solving linear convection-diffusion equations. The method generalizes our previous work on developing the SLDG method for…

Although the performance of commodity computers has improved drastically with the introduction of multicore processors and GPU computing, the standard R distribution is still based on single-threaded model of computation, using only a small…

Discrete optimization is a central problem in artificial intelligence. The optimization of the aggregated cost of a network of cost functions arises in a variety of problems including (W)CSP, DCOP, as well as optimization in stochastic…

Integrating renewable resources within the transmission grid at a wide scale poses significant challenges for economic dispatch as it requires analysis with more optimization parameters, constraints, and sources of uncertainty. This…

Understanding and predicting interface diffusion phenomena in materials is crucial for various industrial applications, including semiconductor manufacturing, battery technology, and catalysis. In this study, we propose a novel approach…

Graph Gaussian Processes (GGPs) provide a data-efficient solution on graph structured domains. Existing approaches have focused on static structures, whereas many real graph data represent a dynamic structure, limiting the applications of…

Graphs are widely used to model relational data. As graphs are getting larger and larger in real-world scenarios, there is a trend to store and compute subgraphs in multiple local systems. For example, recently proposed \emph{subgraph…

Heat diffusion has been widely used in brain imaging for surface fairing, mesh regularization and cortical data smoothing. Motivated by diffusion wavelets and convolutional neural networks on graphs, we present a new fast and accurate…

Local discontinuous Galerkin methods are developed for solving second order and fourth order time-dependent partial differential equations defined on static 2D manifolds. These schemes are second-order accurate with surfaces triangulized by…

Finding influential users in social networks is a fundamental problem with many possible useful applications. Viewing the social network as a graph, the influence of a set of users can be measured by the number of neighbors located within a…

Dynamic urban scene modeling is a rapidly evolving area with broad applications. While current approaches leveraging neural radiance fields or Gaussian Splatting have achieved fine-grained reconstruction and high-fidelity novel view…

Despite the recent success of Graph Neural Networks, it remains challenging to train a GNN on large graphs with millions of nodes and billions of edges, which are prevalent in many graph-based applications. Traditional sampling-based…