CORGI: GNNs with Convolutional Residual Global Interactions for Lagrangian Simulation

TL;DR

CoRGI introduces a lightweight Eulerian CNN module to augment GNN-based Lagrangian solvers, enabling efficient global interaction modeling for CFD. By projecting particle features onto a grid, applying multi-scale CNNs, and reprojecting to particles, it substantially expands the receptive field without prohibitive cost. Across seven Lagrangian CFD tasks, CoRGI consistently improves rollout accuracy and physical plausibility, outperforming both GNS and SEGNN while maintaining favorable runtime trade-offs. The work demonstrates that hybrid particle-grid architectures can capture nonlocal fluid dynamics more effectively than purely local GNNs, with scalable information propagation advantages.

Abstract

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.

Figures (6)

• Figure 1: An illustration of the CoRGI architecture over an example 2D particle dataset. For a GNN with $2L$ layers, our method takes node features encoded by the GNN at layer $L$, processes them into grid-based features at different resolution levels through a scatter operation, and then apply a multi-resolution CNN inspired by U-net ronneberger2015unet to capture global features. After this, the processed grid feature at the highest resolution are mapped back to node features, and finally the latter $L$ layers of GNN message passing decodes the features into outputs.
• Figure 2: Kernel density estimation on DAM-2D ($t \in \llbracket 0, 400\rrbracket$). Above, uniform coloring indicates adherence to fluid incompressibility. Qualitatively, CoRGI maintains lower density variance under turbulent regimes.
• Figure 3: Plot of accuracy compared to inference time for GNS and CoRGI on RPF-2D. Dotted lines pair points based on number of message passing steps. We adjust our allocated time budget in the above plots by adding or removing GNN message passing layers. Due to noise, the relationship is not empirically monotonic, but still demonstrates a trend of CoRGI outperforming GNS for a given time budget.
• Figure 4: Plot of accuracy compared to history for GNS and CoRGI on RPF-2D.
• Figure 5: Plot of accuracy compared to average node degree for GNS and CoRGI on RPF-2D.

Theorems & Definitions (2)

• theorem 1
• proof