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Graph Neural Networks (GNNs) are widely applied to graph learning problems such as node classification. When scaling up the underlying graphs of GNNs to a larger size, we are forced to either train on the complete graph and keep the full…

Graph neural networks (GNNs) work remarkably well in semi-supervised node regression, yet a rigorous theory explaining when and why they succeed remains lacking. To address this gap, we study an aggregate-and-readout model that encompasses…

This work introduces a novel data-driven framework to formulate explicit algebraic Reynolds-averaged Navier-Stokes (RANS) turbulence closures. Recent years have witnessed a blossom in applying machine learning (ML) methods to revolutionize…

Physical systems with complex unsteady dynamics, such as fluid flows, are often poorly represented by a single mean solution. For many practical applications, it is crucial to access the full distribution of possible states, from which…

Graphical models capture relations between entities in a wide range of applications including social networks, biology, and natural language processing, among others. Graph neural networks (GNN) are neural models that operate over graphs,…

To accurately study chemical reactions in the condensed phase or within enzymes, both a quantum-mechanical description and sufficient configurational sampling is required to reach converged estimates. Here, quantum mechanics/molecular…

Gradient descent (GD) methods for the training of artificial neural networks (ANNs) belong nowadays to the most heavily employed computational schemes in the digital world. Despite the compelling success of such methods, it remains an open…

Set-based learning is an essential component of modern deep learning and network science. Graph Neural Networks (GNNs) and their edge-free counterparts Deepsets have proven remarkably useful on ragged and topologically challenging datasets.…

The application of deep learning to symbolic domains remains an active research endeavour. Graph neural networks (GNN), consisting of trained neural modules which can be arranged in different topologies at run time, are sound alternatives…

Large-eddy simulations (LES) require closures for filtered production rates because the resolved fields do not contain all correlations that govern chemical source terms. We develop a graph neural network (GNN) that predicts filtered…

Recently, fine-tuning large-scale pre-trained GNNs has yielded remarkable attention in adapting pre-trained GNN models for downstream graph learning tasks. One representative fine-tuning method is to exploit adapter (termed AdapterGNN)…

Mesh-based Graph Neural Networks (GNNs) have recently shown capabilities to simulate complex multiphysics problems with accelerated performance times. However, mesh-based GNNs require a large number of message-passing (MP) steps and suffer…

Graph neural networks (GNNs), which learn the representation of a node by aggregating its neighbors, have become an effective computational tool in downstream applications. Over-smoothing is one of the key issues which limit the performance…

Graph Neural Networks (GNNs) are powerful tools for addressing learning problems on graph structures, with a wide range of applications in molecular biology and social networks. However, the theoretical foundations underlying their…

In this paper, we design Graph Neural Networks (GNNs) with attention mechanisms to tackle an important yet challenging nonlinear regression problem: massive network localization. We first review our previous network localization method…

Graph Representation Learning (GRL) has experienced significant progress as a means to extract structural information in a meaningful way for subsequent learning tasks. Current approaches including shallow embeddings and Graph Neural…

Graph neural networks (GNNs), which learn the node representations by recursively aggregating information from its neighbors, have become a predominant computational tool in many domains. To handle large-scale graphs, most of the existing…

Graph Neural Networks (GNNs) extend convolutional neural networks to operate on graphs. Despite their impressive performances in various graph learning tasks, the theoretical understanding of their generalization capability is still…

Fluid dynamics spans phenomena from the Cheerios effect to cosmic evolution and has been called the 'queen mother' of science. Traditional modelling relies on numerical methods, including finite differences, volumes, and elements, that…

This work introduces a novel graph neural networks (GNNs)-based method to predict stream water temperature and reduce model bias across locations of different income and education levels. Traditional physics-based models often have limited…