相关论文: Green Multigrid Network

Data fields sampled on irregularly spaced points arise in many applications in the sciences and engineering. For regular grids, Convolutional Neural Networks (CNNs) have been successfully used to gaining benefits from weight sharing and…

This paper studies numerical solutions for parameterized partial differential equations (P-PDEs) with deep learning (DL). P-PDEs arise in many important application areas and the computational cost using traditional numerical schemes can be…

Graph Neural Networks (GNNs) have demonstrated remarkable success in various applications, yet they often struggle to capture long-range dependencies (LRD) effectively. This paper introduces GraphMinNet, a novel GNN architecture that…

Graph neural network (GNN) potentials such as SchNet improve the accuracy and transferability of molecular dynamics (MD) simulation by learning many-body interactions, but remain slower than classical force fields due to fragmented kernels…

Recently, graph convolutional networks (GCNs) have shown great potential for the task of graph matching. It can integrate graph node feature embedding, node-wise affinity learning and matching optimization together in a unified end-to-end…

In this paper, we propose MGNet, a simple and effective multiplex graph convolutional network (GCN) model for multimodal brain network analysis. The proposed method integrates tensor representation into the multiplex GCN model to extract…

Partial differential equations are often used to model various physical phenomena, such as heat diffusion, wave propagation, fluid dynamics, elasticity, electrodynamics and image processing, and many analytic approaches or traditional…

Scientific computing using deep learning has seen significant advancements in recent years. There has been growing interest in models that learn the operator from the parameters of a partial differential equation (PDE) to the corresponding…

Most feedforward convolutional neural networks spend roughly the same efforts for each pixel. Yet human visual recognition is an interaction between eye movements and spatial attention, which we will have several glimpses of an object in…

This article introduces GIT-Net, a deep neural network architecture for approximating Partial Differential Equation (PDE) operators, inspired by integral transform operators. GIT-NET harnesses the fact that differential operators commonly…

Advancement in finite element methods have become essential in various disciplines, and in particular for Computational Fluid Dynamics (CFD), driving research efforts for improved precision and efficiency. While Convolutional Neural…

In the realm of 3D-computer vision applications, point cloud few-shot learning plays a critical role. However, it poses an arduous challenge due to the sparsity, irregularity, and unordered nature of the data. Current methods rely on…

While the celebrated graph neural networks yield effective representations for individual nodes of a graph, there has been relatively less success in extending to the task of graph similarity learning. Recent work on graph similarity…

Algebraic multigrid (AMG) methods are among the most efficient solvers for linear systems of equations and they are widely used for the solution of problems stemming from the discretization of Partial Differential Equations (PDEs). The most…

In this work, we propose a novel meta-learning approach for few-shot classification, which learns transferable prior knowledge across tasks and directly produces network parameters for similar unseen tasks with training samples. Our…

Numerical solvers of Partial Differential Equations (PDEs) are of fundamental significance to science and engineering. To date, the historical reliance on legacy techniques has circumscribed possible integration of big data knowledge and…

The structural analogies of ResNets and Multigrid (MG) methods such as common building blocks like convolutions and poolings where already pointed out by He et al.\ in 2016. Multigrid methods are used in the context of scientific computing…

Operator learning trains a neural network to map functions to functions. An ideal operator learning framework should be mesh-free in the sense that the training does not require a particular choice of discretization for the input functions,…

Accurate maps of Greenland's subglacial bed are essential for sea-level projections, but radar observations are sparse and uneven. We introduce GraphTopoNet, a graph-learning framework that fuses heterogeneous supervision and explicitly…

Convolutional Neural Networks (CNNs) have proven highly effective for edge and mobile vision tasks due to their computational efficiency. While many recent works seek to enhance CNNs with global contextual understanding via…