Related papers: GNN-based physics solver for time-independent PDEs

Equivariant Graph Neural Networks (GNNs) have demonstrated significant success across various applications. To achieve completeness -- that is, the universal approximation property over the space of equivariant functions -- the network must…

Graph neural networks (GNNs) continue to achieve state-of-the-art performance on many graph learning tasks, but rely on the assumption that a given graph is a sufficient approximation of the true neighborhood structure. When a system…

Graph Neural Networks (GNNs) resurge as a trending research subject owing to their impressive ability to capture representations from graph-structured data. However, the black-box nature of GNNs presents a significant challenge in terms of…

This work introduces a new approach for accelerating the numerical analysis of time-domain partial differential equations (PDEs) governing complex physical systems. The methodology is based on a combination of a classical reduced-order…

Graph neural networks (GNNs) have received great attention due to their success in various graph-related learning tasks. Several GNN frameworks have then been developed for fast and easy implementation of GNN models. Despite their…

Deep learning-based approaches have been developed to solve challenging problems in wireless communications, leading to promising results. Early attempts adopted neural network architectures inherited from applications such as computer…

Simulating particle dynamics with high fidelity is crucial for solving real-world interaction and control tasks involving liquids in design, graphics, and robotics. Recently, data-driven approaches, particularly those based on graph neural…

The graph neural network (GNN) has demonstrated its superior performance in various applications. The working mechanism behind it, however, remains mysterious. GNN models are designed to learn effective representations for graph-structured…

Graph neural networks (GNNs) have significantly improved the representation power for graph-structured data. Despite of the recent success of GNNs, the graph convolution in most GNNs have two limitations. Since the graph convolution is…

Graph neural networks (GNNs) have demonstrated their effectiveness in various tasks supported by their generalization capabilities. However, the current analysis of GNN generalization relies on the assumption that training and testing data…

Graph Neural Networks (GNNs) are deep learning models that take graph data as inputs, and they are applied to various tasks such as traffic prediction and molecular property prediction. However, owing to the complexity of the GNNs, it has…

Graph neural networks (GNNs) are powerful tools for developing scalable, decentralized artificial intelligence in large-scale networked systems, such as wireless networks, power grids, and transportation networks. Currently, GNNs in…

Partial differential equations (PDEs) play a crucial role in studying a vast number of problems in science and engineering. Numerically solving nonlinear and/or high-dimensional PDEs is often a challenging task. Inspired by the traditional…

Graph Neural Networks (GNNs) require a relatively large number of labeled nodes and a reliable/uncorrupted graph connectivity structure in order to obtain good performance on the semi-supervised node classification task. The performance of…

Computational Intelligence (CI) techniques have shown great potential as a surrogate model of expensive physics simulation, with demonstrated ability to make fast predictions, albeit at the expense of accuracy in some cases. For many…

We present Graph Neural Diffusion (GRAND) that approaches deep learning on graphs as a continuous diffusion process and treats Graph Neural Networks (GNNs) as discretisations of an underlying PDE. In our model, the layer structure and…

Graph Neural Networks (GNNs) are a promising deep learning approach for circumventing many real-world problems on graph-structured data. However, these models usually have at least one of four fundamental limitations: over-smoothing,…

Message-passing Graph Neural Networks (GNNs) are often criticized for their limited expressiveness, issues like over-smoothing and over-squashing, and challenges in capturing long-range dependencies. Conversely, Graph Transformers (GTs) are…

Molecular dynamics (MD) simulations are a central tool in science and engineering enabling the study of dynamical behavior and the link between microscopic structure and macroscopic function. Their high computational cost, however, has…

Driven by the outstanding performance of neural networks in the structured Euclidean domain, recent years have seen a surge of interest in developing neural networks for graphs and data supported on graphs. The graph is leveraged at each…