Related papers: MG-GNN: Multigrid Graph Neural Networks for Learni…
Graph Neural Networks (GNNs) have become the state-of-the-art method for many applications on graph structured data. GNNs are a model for graph representation learning, which aims at learning to generate low dimensional node embeddings that…
Graph Convolutional Neural Networks (GCNNs) are generalizations of CNNs to graph-structured data, in which convolution is guided by the graph topology. In many cases where graphs are unavailable, existing methods manually construct graphs…
First-order methods such as stochastic gradient descent (SGD) are currently the standard algorithm for training deep neural networks. Second-order methods, despite their better convergence rate, are rarely used in practice due to the…
Utilizing machine learning to address partial differential equations (PDEs) presents significant challenges due to the diversity of spatial domains and their corresponding state configurations, which complicates the task of encompassing all…
Physics-informed neural networks (PINNs) have lately received significant attention as a representative deep learning-based technique for solving partial differential equations (PDEs). Most fully connected network-based PINNs use automatic…
Inspired by the extensive success of deep learning, graph neural networks (GNNs) have been proposed to learn expressive node representations and demonstrated promising performance in various graph learning tasks. However, existing endeavors…
Time series forecasting is an extensively studied subject in statistics, economics, and computer science. Exploration of the correlation and causation among the variables in a multivariate time series shows promise in enhancing the…
Graph Neural Networks (GNNs) became useful for learning on non-Euclidean data. However, their best performance depends on choosing the right model architecture and the training objective, also called the loss function. Researchers have…
Graph neural networks (GNNs) have achieved great success in many scenarios with graph-structured data. However, in many real applications, there are three issues when applying GNNs: graphs are unknown, nodes have noisy features, and graphs…
We describe a computationally efficient, stochastic graph-regularization technique that can be utilized for the semi-supervised training of deep neural networks in a parallel or distributed setting. We utilize a technique, first described…
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…
Graph neural networks (GNNs) demonstrate a robust capability for representation learning on graphs with complex structures, showcasing superior performance in various applications. The majority of existing GNNs employ a graph convolution…
Graph neural networks (GNNs) have become crucial in multimodal recommendation tasks because of their powerful ability to capture complex relationships between neighboring nodes. However, increasing the number of propagation layers in GNNs…
Graph Neural Networks (GNNs) are an emerging research field. This specialized Deep Neural Network (DNN) architecture is capable of processing graph structured data and bridges the gap between graph processing and Deep Learning (DL). As…
Neural networks (NNs) have gained significant attention across various engineering disciplines, particularly in design optimization, where they are used to build surrogate models for high-dimensional regression problems. Despite their power…
Edge intelligence has arisen as a promising computing paradigm for supporting miscellaneous smart applications that rely on machine learning techniques. While the community has extensively investigated multi-tier edge deployment for…
Recent developments in mechanical, aerospace, and structural engineering have driven a growing need for efficient ways to model and analyse structures at much larger and more complex scales than before. While established numerical methods…
Predicting interactions between structured entities lies at the core of numerous tasks such as drug regimen and new material design. In recent years, graph neural networks have become attractive. They represent structured entities as graphs…
We develop a unified model, known as MgNet, that simultaneously recovers some convolutional neural networks (CNN) for image classification and multigrid (MG) methods for solving discretized partial differential equations (PDEs). This model…
Graph Neural Networks (GNNs) are emerging as powerful tools for nonlinear Model Order Reduction (MOR) of time-dependent parameterized Partial Differential Equations (PDEs). However, existing methodologies struggle to combine geometric…