相关论文: Faster Local Solvers for Graph Diffusion Equations

Generating graph-structured data is a challenging problem, which requires learning the underlying distribution of graphs. Various models such as graph VAE, graph GANs, and graph diffusion models have been proposed to generate meaningful and…

This article shows how to develop an efficient solver for a stabilized numerical space-time formulation of the advection-dominated diffusion transient equation. At the discrete space-time level, we approximate the solution by using…

The information diffusion performance of GCN and its variant models is limited by the adjacency matrix, which can lower their performance. Therefore, we introduce a new framework for graph convolutional networks called Hybrid…

While Graph Neural Networks (GNNs) have recently become the de facto standard for modeling relational data, they impose a strong assumption on the availability of the node or edge features of the graph. In many real-world applications,…

We construct deterministic particle solutions for linear and fast diffusion equations using a nonlocal approximation. We exploit the $2$-Wasserstein gradient flow structure of the equations in order to obtain the nonlocal approximating PDEs…

Graph neural networks (GNNs) have shown promising results across various graph learning tasks, but they often assume homophily, which can result in poor performance on heterophilic graphs. The connected nodes are likely to be from different…

Neural networks have proven to be efficient surrogate models for tackling partial differential equations (PDEs). However, their applicability is often confined to specific PDEs under certain constraints, in contrast to classical PDE solvers…

Diffusion models have excelled in generating natural images and are now being adapted to a variety of data types, including graphs. However, conventional models often rely on Gaussian or categorical diffusion processes, which can struggle…

We present multiscale graph-based reduction algorithms for upscaling heterogeneous and anisotropic diffusion problems. The proposed coarsening approaches begin by constructing a partitioning of the computational domain into a set of…

The Graph Edit Distance (GED) problem, which aims to compute the minimum number of edit operations required to transform one graph into another, is a fundamental challenge in graph analysis with wide-ranging applications. However, due to…

Graph generative models have broad applications in biology, chemistry and social science. However, modelling and understanding the generative process of graphs is challenging due to the discrete and high-dimensional nature of graphs, as…

Efficient computation of node proximity queries such as transition probabilities, Personalized PageRank, and Katz are of fundamental importance in various graph mining and learning tasks. In particular, several recent works leverage fast…

Graph Neural Networks (GNNs) are highly vulnerable to adversarial attacks, which can greatly degrade their performance. Existing graph purification methods attempt to address this issue by filtering attacked graphs. However, they struggle…

Graph Convolutional Networks (GCN) is a pioneering model for graph-based semi-supervised learning. However, GCN does not perform well on sparsely-labeled graphs. Its two-layer version cannot effectively propagate the label information to…

The radiation diffusion problem is a kind of {time-dependent} nonlinear equations. For solving the radiation diffusion equations, many linear systems are obtained in the nonlinear iterations at each time step. The cost of linear equations…

Convolutional Neural Networks (CNN) have been regarded as a powerful class of models for visual recognition problems. Nevertheless, the convolutional filters in these networks are local operations while ignoring the large-range dependency.…

With the impressive generative capabilities of diffusion models, personalized content synthesis has emerged as the most highly anticipated. However, the large model sizes and iterative nature of inference make it difficult to deploy…

We demonstrate a high-performance vendor-agnostic method for massively parallel solving of ensembles of ordinary differential equations (ODEs) and stochastic differential equations (SDEs) on GPUs. The method is integrated with a widely used…

The diffusive-viscous wave equation is an advancement in wave equation theory, as it accounts for both diffusion and viscosity effects. This has a wide range of applications in geophysics, such as the attenuation of seismic waves in…

We introduce the framework of continuous-depth graph neural networks (GNNs). Neural graph differential equations (Neural GDEs) are formalized as the counterpart to GNNs where the input-output relationship is determined by a continuum of GNN…