Partial differential equations (PDEs) are central to dynamical systems modeling, particularly in hydrodynamics, where traditional solvers often struggle with nonlinearity and computational cost. Lagrangian neural surrogates such as GNS and SEGNN have emerged as strong alternatives by learning from particle-based simulations. However, these models typically operate with limited receptive fields, making them inaccurate for capturing the inherently global interactions in fluid flows. Motivated by this observation, we introduce Convolutional Residual Global Interactions (CORGI), a hybrid architecture that augments any GNN-based solver with a lightweight Eulerian component for global context aggregation. By projecting particle features onto a grid, applying convolutional updates, and mapping them back to the particle domain, CORGI captures long-range dependencies without significant overhead. When applied to a GNS backbone, CORGI achieves a 57% improvement in rollout accuracy with only 13% more inference time and 31% more training time. Compared to SEGNN, CORGI improves accuracy by 49% while reducing inference time by 48% and training time by 30%. Even under identical runtime constraints, CORGI outperforms GNS by 47% on average, highlighting its versatility and performance on varied compute budgets.

Self-supervised learning is gaining considerable attention as a solution to avoid the requirement of extensive annotations in representation learning on graphs. Current algorithms are based on contrastive learning, which is computation an memory expensive, and the assumption of invariance under certain graph augmentations. However, graph transformations such as edge sampling may modify the semantics of the data so that the iinvariance assumption may be incorrect. We introduce Regularized Graph Infomax (RGI), a simple yet effective framework for node level self-supervised learning that trains a graph neural network encoder by maximizing the mutual information between output node embeddings and their propagation through the graph, which encode the nodes' local and global context, respectively. RGI do not use graph data augmentations but instead generates self-supervision signals with feature propagation, is non-contrastive and does not depend on a two branch architecture. We run RGI on both transductive and inductive settings with popular graph benchmarks and show that it can achieve state-of-the-art performance regardless of its simplicity.