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Solving partial differential equations (PDEs) serves as a cornerstone for modeling complex dynamical systems. Recent progresses have demonstrated grand benefits of data-driven neural-based models for predicting spatiotemporal dynamics…

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…

We propose a unified framework for adaptive connection sampling in graph neural networks (GNNs) that generalizes existing stochastic regularization methods for training GNNs. The proposed framework not only alleviates over-smoothing and…

Recently, machine learning, particularly message-passing graph neural networks (MPNNs), has gained traction in enhancing exact optimization algorithms. For example, MPNNs speed up solving mixed-integer optimization problems by imitating…

While Graph Neural Networks (GNNs) recently became powerful tools in graph learning tasks, considerable efforts have been spent on improving GNNs' structural encoding ability. A particular line of work proposed subgraph GNNs that use…

Training deep graph neural networks (GNNs) poses a challenging task, as the performance of GNNs may suffer from the number of hidden message-passing layers. The literature has focused on the proposals of {over-smoothing} and…

Molecular dynamics (MD) simulations enable the study of the motion of small and large (bio)molecules and the estimation of their conformational ensembles. The description of the environment (solvent) has thereby a large impact. Implicit…

Traffic forecasting is a core element of intelligent traffic monitoring system. Approaches based on graph neural networks have been widely used in this task to effectively capture spatial and temporal dependencies of road networks. However,…

The goal of the state estimation (SE) algorithm is to estimate complex bus voltages as state variables based on the available set of measurements in the power system. Because phasor measurement units (PMUs) are increasingly being used in…

Message Passing Neural Networks (MPNNs) are a common type of Graph Neural Network (GNN), in which each node's representation is computed recursively by aggregating representations (messages) from its immediate neighbors akin to a…

We propose a physics-informed machine learning framework called P-DivGNN to reconstruct local stress fields at the micro-scale, in the context of multi-scale simulation given a periodic micro-structure mesh and mean, macro-scale, stress…

Graph Neural Networks (GNNs) have received considerable attention since its introduction. It has been widely applied in various fields due to its ability to represent graph structured data. However, the application of GNNs is constrained by…

A graph neural network (GNN) approach is introduced in this work which enables mesh-based three-dimensional super-resolution of fluid flows. In this framework, the GNN is designed to operate not on the full mesh-based field at once, but on…

Many real-world physics and engineering problems arise in geometrically complex domains discretized by meshes for numerical simulations. The nodes of these potentially irregular meshes naturally form point clouds whose limited tractability…

Graph matching is a commonly used technique in computer vision and pattern recognition. Recent data-driven approaches have improved the graph matching accuracy remarkably, whereas some traditional algorithm-based methods are more robust to…

Molecular dynamics simulations can generate atomically detailed trajectories of complex systems, but analyzing these dynamics can be challenging when systems lack well-established quantitative descriptors (features). Graph neural networks…

The majority of model-based learned image reconstruction methods in medical imaging have been limited to uniform domains, such as pixelated images. If the underlying model is solved on nonuniform meshes, arising from a finite element method…

We have proposed a self-supervised deep learning framework for solving the mesh blending problem in scenarios where the meshes are not in correspondence. To solve this problem, we have developed Red-Blue MPNN, a novel graph neural network…

The online prediction of multivariate signals, existing simultaneously in space and time, from noisy partial observations is a fundamental task in numerous applications. We propose an efficient Neural Network architecture for the online…

Graph neural networks (GNNs) are widely used as surrogates for costly experiments and first-principles simulations to study the behavior of compounds at atomistic scale, and their architectural complexity is constantly increasing to enable…