Higher Order Graph Attention Probabilistic Walk Networks

Graphs inherently capture dependencies between nodes or variables through their topological structure, with paths between any two nodes indicating a sequential dependency on the nodes traversed. Message Passing Neural Networks (MPNNs) leverage these latent relationships embedded in graph structures, and have become widely adopted across diverse applications. However, many existing methods predominantly rely on local information within the $1$-hop neighborhood. This approach has notable limitations; for example, $1$-hop aggregation schemes inherently lose long-distance information, and are limited in expressive power as defined by the $k$-Weisfeiler-Leman ($k$-WL) isomorphism test. To address these issues, we propose the Higher Order Graphical Attention (HoGA) module, which assigns weights to variable-length paths sampled based on feature-vector diversity, effectively reconstructing the $k$-hop neighborhood. HoGA represents higher-order relationships as a robust form of self-attention, applicable to any single-hop attention mechanism. In empirical studies, applying HoGA to existing attention-based models consistently leads to significant accuracy improvements on benchmark node classification datasets. Furthermore, we observe that the performance degradation typically associated with additional message-passing steps may be mitigated.

A 3D super-resolution of wind fields via physics-informed pixel-wise self-attention generative adversarial network

To mitigate global warming, greenhouse gas sources need to be resolved at a high spatial resolution and monitored in time to ensure the reduction and ultimately elimination of the pollution source. However, the complexity of computation in resolving high-resolution wind fields left the simulations impractical to test different time lengths and model configurations. This study presents a preliminary development of a physics-informed super-resolution (SR) generative adversarial network (GAN) that super-resolves the three-dimensional (3D) low-resolution wind fields by upscaling x9 times. We develop a pixel-wise self-attention (PWA) module that learns 3D weather dynamics via a self-attention computation followed by a 2D convolution. We also employ a loss term that regularizes the self-attention map during pretraining, capturing the vertical convection process from input wind data. The new PWA SR-GAN shows the high-fidelity super-resolved 3D wind data, learns a wind structure at the high-frequency domain, and reduces the computational cost of a high-resolution wind simulation by x89.7 times.