CoLEP: Co-Evolving Particles and Persistent Eulerian Latent Fields for Neural Fluid Simulation

Graph neural networks (GNNs) have emerged as a powerful framework for learning particle-based fluid dynamics. However, GNN-based simulators suffer from rapid error accumulation over long rollouts and the high computational cost of repeated message passing. We introduce CoLEP, a co-evolving Lagrangian–Eulerian particle simulator that augments particle-carried states with a persistent latent field on a fixed Eulerian grid. At each step, current particle information updates the inherited Eulerian state, which is then fed back to guide particle prediction, allowing spatial interaction context to accumulate and be reused across time. Building on this persistent state, we introduce periodic GNN skipping (PGS), which interleaves full graph-based interaction updates with learned graph-free Fast steps while continuing to evolve both the particle and Eulerian states. Across four particle-simulation benchmarks, CoLEP consistently improves long-horizon rollout accuracy over the evaluated baselines. Eulerian state ablations further show that persistence is particularly important when graph evaluations are sparse, while PGS provides a favorable accuracy–inference-cost trade-off.