Related papers: Adaptive Graph Rewiring to Mitigate Over-Squashing…

Computational Fluid Dynamics (CFD) is widely used in different engineering fields, but accurate simulations are dependent upon proper meshing of the simulation domain. While highly refined meshes may ensure precision, they come with high…

Graph Neural Networks (GNNs) have been shown to achieve competitive results to tackle graph-related tasks, such as node and graph classification, link prediction and node and graph clustering in a variety of domains. Most GNNs use a message…

Most graph neural networks (GNNs) use the message passing paradigm, in which node features are propagated on the input graph. Recent works pointed to the distortion of information flowing from distant nodes as a factor limiting the…

Machine Learning surrogates for Computational Fluid Dynamics (CFD), particularly Graph Neural Networks (GNNs) and Transformers, have become a new important approach for accelerating physics simulations. However, we identify a critical…

Graph Neural Networks (GNNs) are models that leverage the graph structure to transmit information between nodes, typically through the message-passing operation. While widely successful, this approach is well known to suffer from the…

Time-independent Partial Differential Equations (PDEs) on large meshes pose significant challenges for data-driven neural PDE solvers. We introduce a novel graph rewiring technique to tackle some of these challenges, such as aggregating…

Graph Neural Networks (GNNs) are popular machine learning methods for modeling graph data. A lot of GNNs perform well on homophily graphs while having unsatisfactory performance on heterophily graphs. Recently, some researchers turn their…

Physics-informed Graph Neural Networks have achieved remarkable performance in learning through graph-structured data by mitigating common GNN challenges such as over-smoothing, over-squashing, and heterophily adaption. Despite these…

Simulating physics using Graph Neural Networks (GNNs) is predominantly driven by message-passing architectures, which face challenges in scaling and efficiency, particularly in handling large, complex meshes. These architectures have…

Message Passing Neural Networks (MPNNs) are instances of Graph Neural Networks that leverage the graph to send messages over the edges. This inductive bias leads to a phenomenon known as over-squashing, where a node feature is insensitive…

Graph neural networks (GNNs) are able to leverage the structure of graph data by passing messages along the edges of the graph. While this allows GNNs to learn features depending on the graph structure, for certain graph topologies it leads…

Graph neural networks (GNNs) have achieved strong performance across various real-world domains. Nevertheless, they suffer from oversquashing, where long-range information is distorted as it is compressed through limited message-passing…

Message passing graph neural networks (GNNs) are a popular learning architectures for graph-structured data. However, one problem GNNs experience is oversquashing, where a GNN has difficulty sending information between distant nodes.…

The quality of signal propagation in message-passing graph neural networks (GNNs) strongly influences their expressivity as has been observed in recent works. In particular, for prediction tasks relying on long-range interactions, recursive…

Most graph neural networks (GNNs) are prone to the phenomenon of over-squashing in which node features become insensitive to information from distant nodes in the graph. Recent works have shown that the topology of the graph has the…

Graph Neural Networks have recently become a prevailing paradigm for various high-impact graph analytical problems. Existing efforts can be mainly categorized as spectral-based and spatial-based methods. The major challenge for the former…

Nonlinear finite element crash simulations are accurate but computationally expensive, limiting their use in iterative design optimisation. Machine-learning surrogate models based on graph neural networks (GNNs) offer a faster alternative.…

Over-squashing is a challenge in training graph neural networks for tasks involving long-range dependencies. In such tasks, a GNN's receptive field should be large enough to enable communication between distant nodes. However, gathering…

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…

Meshing is a critical, but user-intensive process necessary for stable and accurate simulations in computational fluid dynamics (CFD). Mesh generation is often a bottleneck in CFD pipelines. Adaptive meshing techniques allow the mesh to be…