Related papers: Graph Neural Ordinary Differential Equations for P…

Multimodal graphs are gaining increasing attention due to their rich representational power and wide applicability, yet they introduce substantial challenges arising from severe modality confusion. To address this issue, we propose NSG…

It has been observed that message-passing graph neural networks (GNN) sometimes struggle to maintain a healthy balance between the efficient/scalable modeling of long-range dependencies across nodes while avoiding unintended consequences…

Recent graph neural networks (GNN) has achieved remarkable performance in node representation learning. One key factor of GNN's success is the \emph{smoothness} property on node representations. Despite this, most GNN models are fragile to…

In the quest to improve efficiency, interdependence and complexity are becoming defining characteristics of modern complex networks representing engineered and natural systems. Graph theory is a widely used framework for modeling such…

Graph neural networks (GNNs) have shown advantages in graph-based analysis tasks. However, most existing methods have the homogeneity assumption and show poor performance on heterophilic graphs, where the linked nodes have dissimilar…

Neural ordinary differential equations (neural ODEs) have emerged as a novel network architecture that bridges dynamical systems and deep learning. However, the gradient obtained with the continuous adjoint method in the vanilla neural ODE…

Learning complex network dynamics is fundamental to understanding, modelling and controlling real-world complex systems. There are two main problems in the task of predicting the dynamic evolution of complex networks: on the one hand,…

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…

With the rapid growth of graph-structured data in critical domains, unsupervised graph-level anomaly detection (UGAD) has become a pivotal task. UGAD seeks to identify entire graphs that deviate from normal behavioral patterns. However,…

Fractional Differential Equations (FDEs) are essential tools for modelling complex systems in science and engineering. They extend the traditional concepts of differentiation and integration to non-integer orders, enabling a more precise…

Neural ordinary differential equations (NODEs) are geometric deep learning models based on dynamical systems and flows generated by vector fields on manifolds. Despite numerous successful applications, particularly within the flow matching…

We propose an end-to-end framework based on a Graph Neural Network (GNN) to balance the power flows in energy grids. The balancing is framed as a supervised vertex regression task, where the GNN is trained to predict the current and power…

A hallmark of graph neural networks is their ability to distinguish the isomorphism class of their inputs. This study derives hardness results for the classification variant of graph isomorphism in the message-passing model (MPNN). MPNN…

Graph and hypergraph representation learning has attracted increasing attention from various research fields. Despite the decent performance and fruitful applications of Graph Neural Networks (GNNs), Hypergraph Neural Networks (HGNNs), and…

Identifying accurate dynamic models is required for the simulation and control of various technical systems. In many important real-world applications, however, the two main modeling approaches often fail to meet requirements: first…

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…

This letter devises Neural Dynamic Equivalence (NeuDyE), which explores physics-aware machine learning and neural-ordinary-differential-equations (ODE-Net) to discover a dynamic equivalence of external power grids while preserving its…

Traditional grid analytics are model-based, relying strongly on accurate models of power systems, especially the dynamic models of generators, controllers, loads and other dynamic components. However, acquiring thorough power system models…

Data-driven graph learning models a network by determining the strength of connections between its nodes. The data refers to a graph signal which associates a value with each graph node. Existing graph learning methods either use simplified…

The proposed approach yields a numerical method that provably executes in linear time with respect to the number of nodes and edges in a graph. The graph, constructed from the power system model, requires only knowledge of the dependencies…