# CORGI: GNNs with Convolutional Residual Global Interactions for Lagrangian Simulation

arXiv: https://arxiv.org/abs/2511.22938 · HTML: https://mlsanity.com/paper/2511.22938/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 74 references that are in the map.
- First posted on arXiv 28 Nov 2025.

## Builds on (most cited first, 30 of 32)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Instance Normalization: The Missing Ingredient for Fast Stylization](https://mlsanity.com/paper/1607.08022/) (2016)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [Interaction Networks for Learning about Objects, Relations and Physics](https://mlsanity.com/paper/1612.00222/) (2016)
- [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021)
- [Equivariant message passing for the prediction of tensorial properties and molecular spectra](https://mlsanity.com/paper/2102.03150/) (2021)
- [Choose a Transformer: Fourier or Galerkin](https://mlsanity.com/paper/2105.14995/) (2021)
- [GNOT: A General Neural Operator Transformer for Operator Learning](https://mlsanity.com/paper/2302.14376/) (2023)
- [Geometry-Informed Neural Operator for Large-Scale 3D PDEs](https://mlsanity.com/paper/2309.00583/) (2023)
- [Transformer for Partial Differential Equations' Operator Learning](https://mlsanity.com/paper/2205.13671/) (2022)
- [Cormorant: Covariant Molecular Neural Networks](https://mlsanity.com/paper/1906.04015/) (2019)
- [Factorized Fourier Neural Operators](https://mlsanity.com/paper/2111.13802/) (2021)
- [Geometric and Physical Quantities Improve E(3) Equivariant Message Passing](https://mlsanity.com/paper/2110.02905/) (2021)
- [A guide to convolution arithmetic for deep learning](https://mlsanity.com/paper/1603.07285/) (2016)
- [DPOT: Auto-Regressive Denoising Operator Transformer for Large-Scale PDE Pre-Training](https://mlsanity.com/paper/2403.03542/) (2024)
- [Guaranteed Conservation of Momentum for Learning Particle-based Fluid Dynamics](https://mlsanity.com/paper/2210.06036/) (2022)
- [LagrangeBench: A Lagrangian Fluid Mechanics Benchmarking Suite](https://mlsanity.com/paper/2309.16342/) (2023)
- [Neural SPH: Improved Neural Modeling of Lagrangian Fluid Dynamics](https://mlsanity.com/paper/2402.06275/) (2024)
- [Diffusion-Based Hierarchical Graph Neural Networks for Simulating Nonlinear Solid Mechanics](https://mlsanity.com/paper/2506.06045/) (2025)
- [EddyFormer: Accelerated Neural Simulations of Three-Dimensional Turbulence at Scale](https://mlsanity.com/paper/2510.24173/) (2025)
- [Improving Long-Range Interactions in Graph Neural Simulators via Hamiltonian Dynamics](https://mlsanity.com/paper/2511.08185/) (2025)
- [A Neural Material Point Method for Particle-based Emulation](https://mlsanity.com/paper/2408.15753/) (2024)
- [Symmetric Basis Convolutions for Learning Lagrangian Fluid Mechanics](https://mlsanity.com/paper/2403.16680/) (2024)

## Built on by (most cited first, 1 of 1)

- [Physics-Informed Graph Neural Network Surrogates for Turbulent Nanoparticle Dispersion in Dental Clinical Environments](https://mlsanity.com/paper/2605.19589/) (2026)

## Abstract (arXiv)

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.