Related papers: The G\^ateaux-Hopfield Neural Network method

This paper introduces a novel two-stream deep model based on graph convolutional network (GCN) architecture and feed-forward neural networks (FFNN) for learning the solution of nonlinear partial differential equations (PDEs). The model aims…

The extreme learning machine (ELM) method can yield highly accurate solutions to linear/nonlinear partial differential equations (PDEs), but requires the last hidden layer of the neural network to be wide to achieve a high accuracy. If the…

Graph Neural Networks (GNNs) have emerged as a dominant paradigm for graph classification. Specifically, most existing GNNs mainly rely on the message passing strategy between neighbor nodes, where the expressivity is limited by the…

Graph Neural Networks (GNNs) are well-suited for learning on homophilous graphs, i.e., graphs in which edges tend to connect nodes of the same type. Yet, achievement of consistent GNN performance on heterophilous graphs remains an open…

A set of fixed points of the Hopfield type neural network was under investigation. Its connection matrix is constructed with regard to the Hebb rule from a highly symmetric set of the memorized patterns. Depending on the external parameter…

We introduce Hyperdimensional Graph Learner (HDGL), a novel method for node classification and link prediction in graphs. HDGL maps node features into a very high-dimensional space (\textit{hyperdimensional} or HD space for short) using the…

Solutions to differential equations are of significant scientific and engineering relevance. Recently, there has been a growing interest in solving differential equations with neural networks. This work develops a novel method for solving…

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,…

This paper proposes fractional order graph neural networks (FGNNs), optimized by the approximation strategy to address the challenges of local optimum of classic and fractional graph neural networks which are specialised at aggregating…

Graph Neural Networks (GNNs) traditionally employ a message-passing mechanism that resembles diffusion over undirected graphs, which often leads to homogenization of node features and reduced discriminative power in tasks such as node…

De novo molecular design attempts to search over the chemical space for molecules with the desired property. Recently, deep learning has gained considerable attention as a promising approach to solve the problem. In this paper, we propose…

We propose a novel solution to addressing a long-standing dilemma in the representation learning of graph neural networks (GNNs): how to effectively capture and represent useful information embedded in long-distance nodes to improve the…

An emerging trend in deep learning research focuses on the applications of graph neural networks (GNNs) for mesh-based continuum mechanics simulations. Most of these learning frameworks operate on graphs wherein each edge connects two…

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

This paper presents HGEN that pioneers ensemble learning for heterogeneous graphs. We argue that the heterogeneity in node types, nodal features, and local neighborhood topology poses significant challenges for ensemble learning,…

Conventional AC Power Flow (ACPF) solvers like Newton-Raphson (NR) face significant computational and convergence challenges in modern, large-scale power systems. This paper proposes a novel, two-stage hybrid method that integrates a…

Heterogeneous graph neural network (HGNN) is a very popular technique for the modeling and analysis of heterogeneous graphs. Most existing HGNN-based approaches are supervised or semi-supervised learning methods requiring graphs to be…

We introduce a novel variant of GNN for particle tracking called Hierarchical Graph Neural Network (HGNN). The architecture creates a set of higher-level representations which correspond to tracks and assigns spacepoints to these tracks,…

As a variant of Graph Neural Networks (GNNs), Unfolded GNNs offer enhanced interpretability and flexibility over traditional designs. Nevertheless, they still suffer from scalability challenges when it comes to the training cost. Although…

This letter presents a novel high impedance fault (HIF) detection approach using a convolutional neural network (CNN). Compared to traditional artificial neural networks, a CNN offers translation invariance and it can accurately detect HIFs…