Related papers: Physics-Embedded Neural Networks: Graph Neural PDE…

Partial Differential Equations (PDEs) are central to modeling complex systems across physical, biological, and engineering domains, yet traditional numerical methods often struggle with high-dimensional or complex problems. Physics-Informed…

Graph neural networks (GNN) have shown outstanding applications in many fields where data is fundamentally represented as graphs (e.g., chemistry, biology, recommendation systems). In this vein, communication networks comprise many…

Many interesting datasets ubiquitous in machine learning and deep learning can be described via graphs. As the scale and complexity of graph-structured datasets increase, such as in expansive social networks, protein folding, chemical…

Graph Neural Networks (GNNs) have emerged as a notorious alternative to address learning problems dealing with non-Euclidean datasets. However, although most works assume that the graph is perfectly known, the observed topology is prone to…

The recent introduction of Graph Neural Networks (GNNs) and their growing popularity in the past few years has enabled the application of deep learning algorithms to non-Euclidean, graph-structured data. GNNs have achieved state-of-the-art…

Graph Neural Networks (GNN) have shown a strong potential to be integrated into commercial products for network control and management. Early works using GNN have demonstrated an unprecedented capability to learn from different network…

The successful integration of machine learning models into decision support tools for grid operation hinges on effectively capturing the topological changes in daily operations. Frequent grid reconfigurations and N-k security analyses have…

One of the main challenges in using deep learning-based methods for simulating physical systems and solving partial differential equations (PDEs) is formulating physics-based data in the desired structure for neural networks. Graph neural…

This short note describes the concept of guided training of deep neural networks (DNNs) to learn physically reasonable solutions. DNNs are being widely used to predict phenomena in physics and mechanics. One of the issues of DNNs is that…

Physics-Informed Neural Network (PINN) is a novel multi-task learning framework useful for solving physical problems modeled using differential equations (DEs) by integrating the knowledge of physics and known constraints into the…

Graph neural networks (GNNs) have been applied into a variety of graph tasks. Most existing work of GNNs is based on the assumption that the given graph data is optimal, while it is inevitable that there exists missing or incomplete edges…

Learning continuous-time dynamics on complex networks is crucial for understanding, predicting and controlling complex systems in science and engineering. However, this task is very challenging due to the combinatorial complexities in the…

Machine learning (ML) and deep learning (DL) techniques have gained significant attention as reduced order models (ROMs) to computationally expensive structural analysis methods, such as finite element analysis (FEA). Graph neural network…

We present a Graph Neural Network (GNN) that accurately simulates a multidisperse suspension of interacting spherical particles. Our machine learning framework is built upon the recent work of Sanchez-Gonzalez et al. ICML, PMLR, 119,…

State estimation is highly critical for accurately observing the dynamic behavior of the power grids and minimizing risks from cyber threats. However, existing state estimation methods encounter challenges in accurately capturing power…

Deep learning's performance has been extensively recognized recently. Graph neural networks (GNNs) are designed to deal with graph-structural data that classical deep learning does not easily manage. Since most GNNs were created using…

Graph-structured data consisting of objects (i.e., nodes) and relationships among objects (i.e., edges) are ubiquitous. Graph-level learning is a matter of studying a collection of graphs instead of a single graph. Traditional graph-level…

Substitution of well-grounded theoretical models by data-driven predictions is not as simple in engineering and sciences as it is in social and economic fields. Scientific problems suffer most times from paucity of data, while they may…

Continuum mechanics simulators, numerically solving one or more partial differential equations, are essential tools in many areas of science and engineering, but their performance often limits application in practice. Recent modern machine…

Graph neural networks (GNNs) are the most widely adopted model in graph-structured data oriented learning and representation. Despite their extraordinary success in real-world applications, understanding their working mechanism by theory is…