CoRGI: GNNs with Convolutional Residual Global Interactions for Lagrangian Simulation

Partial differential equations (PDEs) govern dynamical systems in hydrodynamics, where classical solvers face well-known difficulties with nonlinearity and computational cost. Lagrangian neural surrogates such as GNS and SEGNN learn directly from particle-based simulations, but local message passing alone is limited in its ability to represent inherently global flow interactions. We therefore frame neural Lagrangian simulation as a coarse--fine interaction problem: fine-grained local particle dynamics should be coupled with a coarse global pathway. We instantiate this idea with Convolutional Residual Global Interactions (øurs), which projects particle features to an Eulerian grid, applies residual global updates, and maps them back to particles. In this paper, the local/global pair is GNS+CNN, but in principle, the coupling interface is modular and not tied to that specific choice. With a GNS backbone, øurs improves rollout accuracy by 62% with 13% more inference time and 31% more training time. Compared to SEGNN, øurs improves accuracy by 56% while reducing inference time by 48% and training time by 31%. Under matched runtime budgets, øurs still outperforms GNS by 47% on average, supporting the hypothesis that jointly modeling coarse and fine interactions is an effective strategy for neural CFD surrogates.