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Recently, graph-based models designed for downstream tasks have significantly advanced research on graph neural networks (GNNs). GNN baselines based on neural message-passing mechanisms such as GCN and GAT perform worse as the network…
The optimization of well locations and controls is an important step in the design of subsurface flow operations such as oil production or geological CO2 storage. These optimization problems can be computationally expensive, however, as…
This paper explores the applications and challenges of graph neural networks (GNNs) in processing complex graph data brought about by the rapid development of the Internet. Given the heterogeneity and redundancy problems that graph data…
The existing graph neural networks (GNNs) based on the spectral graph convolutional operator have been criticized for its performance degradation, which is especially common for the models with deep architectures. In this paper, we further…
Scientific computing using deep learning has seen significant advancements in recent years. There has been growing interest in models that learn the operator from the parameters of a partial differential equation (PDE) to the corresponding…
This study develops and validates neural network frameworks with physics-based constraints for surrogate modeling of rarefied gas dynamics across different levels of complexity. As a baseline, we first examine the BGK kinetic relaxation…
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…
Subsurface simulations use computational models to predict the flow of fluids (e.g., oil, water, gas) through porous media. These simulations are pivotal in industrial applications such as petroleum production, where fast and accurate…
Graph Neural Network (GNN) is an emerging technique for graph-based learning tasks such as node classification. In this work, we reveal the vulnerability of GNN to the imbalance of node labels. Traditional solutions for imbalanced…
The deep neural network multigrid solver (DNN-MG) combines a coarse-grid finite element simulation with a deep neural network that corrects the solution on finer grid levels, thereby improving the computational efficiency. In this work, we…
Graph convolutional neural networks (GCNs) embed nodes in a graph into Euclidean space, which has been shown to incur a large distortion when embedding real-world graphs with scale-free or hierarchical structure. Hyperbolic geometry offers…
In this paper, we present a graph neural networks (GNNs)-based fast solver (GraphSolver) for solving combined field integral equations (CFIEs) of 3D conducting bodies. Rao-Wilton-Glisson (RWG) basis functions are employed to discretely and…
In the recent years, the domain of fast flow field prediction has been vastly dominated by pixel-based convolutional neural networks. Yet, the recent advent of graph convolutional neural networks (GCNNs) have attracted a considerable…
Reliable evaluations of geotechnical hazards like landslides and debris flow require accurate simulation of granular flow dynamics. Traditional numerical methods can simulate the complex behaviors of such flows that involve solid-like to…
Graph representation learning resurges as a trending research subject owing to the widespread use of deep learning for Euclidean data, which inspire various creative designs of neural networks in the non-Euclidean domain, particularly…
Graph Neural Networks (GNNs) have become a prevailing tool for learning physical dynamics. However, they still encounter several challenges: 1) Physical laws abide by symmetry, which is a vital inductive bias accounting for model…
This paper investigates the feasibility of using Graph Neural Networks (GNNs) for classical motion planning problems. We propose guiding both continuous and discrete planning algorithms using GNNs' ability to robustly encode the topology of…
Deep learning methods for graphs achieve remarkable performance on many node-level and graph-level prediction tasks. However, despite the proliferation of the methods and their success, prevailing Graph Neural Networks (GNNs) neglect…
The study of uncertainty propagation poses a great challenge to design numerical solvers with high fidelity. Based on the stochastic Galerkin formulation, this paper addresses the idea and implementation of the first flux reconstruction…
Sensing the fluid flow around an arbitrary geometry entails extrapolating from the physical quantities perceived at its surface in order to reconstruct the features of the surrounding fluid. This is a challenging inverse problem, yet one…