Related papers: Spatio-spectral graph neural operator for solving …

Partial Differential Equation (PDE) problems often exhibit strong local spatial structures, and effectively capturing these structures is critical for approximating their solutions. Recently, the Fourier Neural Operator (FNO) has emerged as…

The spatial convolution layer which is widely used in the Graph Neural Networks (GNNs) aggregates the feature vector of each node with the feature vectors of its neighboring nodes. The GNN is not aware of the locations of the nodes in the…

Effective node representation lies at the heart of Graph Neural Networks (GNNs), as it directly impacts their ability to perform downstream tasks such as node classification and link prediction. Most existing GNNs, particularly message…

Graph Convolutional Networks (GCNs), similarly to Convolutional Neural Networks (CNNs), are typically based on two main operations - spatial and point-wise convolutions. In the context of GCNs, differently from CNNs, a pre-determined…

Neural operators have become increasingly popular in solving \textit{partial differential equations} (PDEs) due to their superior capability to capture intricate mappings between function spaces over complex domains. However, the…

To capture spatial relationships and temporal dynamics in traffic data, spatio-temporal models for traffic forecasting have drawn significant attention in recent years. Most of the recent works employed graph neural networks(GNN) with…

Solving Singularly Perturbed Differential Equations (SPDEs) poses computational challenges arising from the rapid transitions in their solutions within thin regions. The effectiveness of deep learning in addressing differential equations…

We explore the use of graph neural networks (GNNs) to model spatial processes in which there is no a priori graphical structure. Similar to finite element analysis, we assign nodes of a GNN to spatial locations and use a computational…

Variants of Graph Neural Networks (GNNs) for representation learning have been proposed recently and achieved fruitful results in various fields. Among them, Graph Attention Network (GAT) first employs a self-attention strategy to learn…

We present a novel graph-informed transformer operator (GITO) architecture for learning complex partial differential equation systems defined on irregular geometries and non-uniform meshes. GITO consists of two main modules: a hybrid graph…

Fourier neural operators (FNOs) can learn highly nonlinear mappings between function spaces, and have recently become a popular tool for learning responses of complex physical systems. However, to achieve good accuracy and efficiency, FNOs…

By recursively summing node features over entire neighborhoods, spatial graph convolution operators have been heralded as key to the success of Graph Neural Networks (GNNs). Yet, despite the multiplication of GNN methods across tasks and…

Graph Neural Networks (GNNs) have demonstrated remarkable success across diverse tasks. However, their generalization capability is often hindered by spurious correlations between node features and labels in the graph. Our analysis reveals…

Spatial-temporal forecasting has attracted tremendous attention in a wide range of applications, and traffic flow prediction is a canonical and typical example. The complex and long-range spatial-temporal correlations of traffic flow bring…

In recent years, there has been notable interest in investigating combinatorial optimization (CO) problems by neural-based framework. An emerging strategy to tackle these challenging problems involves the adoption of graph neural networks…

Current neural operators often struggle to generalize to complex, out-of-distribution conditions, limiting their ability in seismic wavefield representation. To address this, we propose a generative neural operator (GNO) that leverages…

Convolutional neural networks (CNNs) have achieved remarkable performance in hyperspectral image (HSI) classification over the last few years. Despite the progress that has been made, rich and informative spectral information of HSI has…

Graph Neural Networks (GNNs) have recently been explored as surrogate models for numerical simulations. While their applications in computational fluid dynamics have been investigated, little attention has been given to structural problems,…

Graph Convolutional Networks (GCNs) have recently become the primary choice for learning from graph-structured data, superseding hash fingerprints in representing chemical compounds. However, GCNs lack the ability to take into account the…

Graph neural networks have emerged as a powerful tool for learning spatiotemporal interactions. However, conventional approaches often rely on predefined graphs, which may obscure the precise relationships being modeled. Additionally,…