Related papers: The G\^ateaux-Hopfield Neural Network method
Recently proposed Gated Linear Networks present a tractable nonlinear network architecture, and exhibit interesting capabilities such as learning with local error signals and reduced forgetting in sequential learning. In this work, we…
A feedforward neural network, including hidden layers, motivated by nonlinear functions (such as Tanh, ReLU, and Sigmoid functions), exhibits uniform approximation properties in Sobolev space, and discontinuous neural networks can reduce…
This study proposes a novel heterogeneous graph convolutional neural network (HGCNN) to handle complex brain fMRI data at regional and across-region levels. We introduce a generic formulation of spectral filters on heterogeneous graphs by…
Recently, graph neural networks have shown the superiority of modeling the complex topological structures in heterogeneous network-based recommender systems. Due to the diverse interactions among nodes and abundant semantics emerging from…
Graph neural networks (GNNs) have achieved great success in various graph problems. However, most GNNs are Message Passing Neural Networks (MPNNs) based on the homophily assumption, where nodes with the same label are connected in graphs.…
Solving the optimal power flow (OPF) problem is a fundamental task to ensure the system efficiency and reliability in real-time electricity grid operations. We develop a new topology-informed graph neural network (GNN) approach for…
We propose a hierarchical graph neural network (GNN) model that learns how to cluster a set of images into an unknown number of identities using a training set of images annotated with labels belonging to a disjoint set of identities. Our…
Graph Neural Networks (GNNs) are effective tools for graph representation learning. Most GNNs rely on a recursive neighborhood aggregation scheme, named message passing, thereby their theoretical expressive power is limited to the…
Graph neural networks (GNN) suffer from severe inefficiency. It is mainly caused by the exponential growth of node dependency with the increase of layers. It extremely limits the application of stochastic optimization algorithms so that the…
We propose a numerical method for solving high dimensional fully nonlinear partial differential equations (PDEs). Our algorithm estimates simultaneously by backward time induction the solution and its gradient by multi-layer neural…
Artificial neural networks are powerful pattern classifiers; however, they have been surpassed in accuracy by methods such as support vector machines and random forests that are also easier to use and faster to train. Backpropagation, which…
Over the past few years, neural network methods have evolved in various directions for approximating partial differential equations (PDEs). A promising new development is the integration of neural networks with classical numerical…
Building on our previous work on Fredholm Neural Networks (Fredholm NNs/ FNNs) for solving integral equations, we extend the framework to inverse problems for linear and nonlinear elliptic partial differential equations. The proposed scheme…
We propose a Graph Neural Network with greater expressive power than commonly used GNNs - not constrained to only differentiate between graphs that Weisfeiler-Lehman test recognizes to be non-isomorphic. We use a graph attention network…
In this work, we use the finite differences in time domain (FDTD) numerical method to compute and assess the validity of Hopf solutions, or hopfions, for the electromagnetic field equations. In these solutions, field lines form closed loops…
Distributed training of graph neural networks (GNNs) has become a crucial technique for processing large graphs. Prevalent GNN frameworks are model-centric, necessitating the transfer of massive graph vertex features to GNN models, which…
We propose the Gaussian Gated Linear Network (G-GLN), an extension to the recently proposed GLN family of deep neural networks. Instead of using backpropagation to learn features, GLNs have a distributed and local credit assignment…
In this work, we present a hybrid numerical method for solving evolution partial differential equations (PDEs) by merging the time finite element method with deep neural networks. In contrast to the conventional deep learning-based…
This paper presents a novel hybrid approach for modeling the voltage gain of LLC resonant converters by combining deep-learning neural networks with the polynomial based Group Method of Data Handling (GMDH). While deep learning offers high…
Spectral graph convolutional neural networks (GCNNs) have been producing encouraging results in graph classification tasks. However, most spectral GCNNs utilize fixed graphs when aggregating node features, while omitting edge feature…