The field of environmental modeling and prediction is witnessing significant advancements, driven by innovations in graph neural networks, hybrid neural architectures, and novel rewiring methods. These developments are improving the accuracy and reliability of predictions in various domains, including fluid dynamics, oceanic modeling, air traffic management, and climate forecasting. A key trend is the integration of physical correlations and graph topology to mitigate issues such as over-squashing in mesh graph neural networks. Another notable direction is the employment of deformable convolution networks and terrain-adaptive mask constraints to model complex spatial dependencies and multi-scale characteristics in oceanic and atmospheric phenomena. The use of probabilistic approaches, such as 3-D Gaussian Mixture Models, is also gaining traction for capturing uncertainty in weather forecasting and air traffic prediction. Furthermore, graph neural networks are being leveraged to post-process ensemble forecasts and enhance forecast accuracy for extreme weather events. Noteworthy papers include:

• PIORF, which proposes a novel rewiring method for mesh graph neural networks, achieving up to 26.2% improvement in fluid dynamics benchmark datasets.
• KunPeng, which constructs a global ocean environmental prediction model, achieving significant improvements in sea surface parameter prediction and deep-sea region characterization.
• Handling Weather Uncertainty in Air Traffic Prediction through an Inverse Approach, which introduces a 3-D Gaussian Mixture Model to predict long lead-time flight trajectory changes, demonstrating robust performance and scalability.
• Graph Neural Networks for Enhancing Ensemble Forecasts of Extreme Rainfall, which presents a novel framework for post-processing ensemble forecasts using graph neural networks, improving forecast accuracy for extreme weather events.
• Drought forecasting using a hybrid neural architecture, which achieves state-of-the-art performance on the DroughtED dataset and presents reliable prediction of USDM categories.