Hybrid Lagrangian-Eulerian Model for Lagrangian Fluid Simulation

2026-08-02

AI Summary

Purely Lagrangian neural fluid simulations suffer from spatial redundancy and temporal trajectory drift: uniform regions waste model capacity, while the absence of a global reference leads to error accumulation over time. To address these limitations, this work proposes the first neural fluid framework that seamlessly integrates Lagrangian particles with an Eulerian grid. The method employs adaptive downsampling to preserve fine-scale details while compressing large-scale features onto a fixed grid, and introduces a grid-based cross-attention mechanism that anchors particle trajectories to the Eulerian grid at each time step for consistent correction. This approach substantially alleviates spatial inefficiency and temporal drift, achieving state-of-the-art accuracy and stability in long-horizon rollouts.

Abstract

Pure Lagrangian neural simulators offer geometric flexibility and exact advection, making them well-suited for modeling moving domains and free surfaces. However, the absence of a fixed global reference frame introduces two severe limitations: a spatial bottleneck, in which model capacity is wasted on uniform regions because the dense particle neighborhoods required for stable gradients are applied indiscriminately, and rapid temporal drift, caused by purely local message passing that lacks a global anchor. Inspired by classical hybrid numerical solvers, we propose a Hybrid Lagrangian-Eulerian neural simulator that augments Lagrangian dynamics with an Eulerian representation. To address the spatial bottleneck, we introduce adaptive downsampling that eliminates kinematic redundancy, preserving micro-scale details on particles while aggregating compressed features onto Eulerian nodes to resolve large-scale dynamics. To counter temporal drift, we employ a cross-attention mechanism that queries these Eulerian features, using the fixed grid as a stable spatial anchor to correct trajectory deviations at every timestep. Comprehensive experiments show that this hierarchical, cross-attended design substantially suppresses error accumulation, establishing a new state-of-the-art for accuracy and rollout stability in Lagrangian fluid simulation.

Problem

• Lagrangian fluid simulation
• spatial bottleneck
• temporal drift
• global reference frame
• neural simulators

Innovation

• Hybrid Lagrangian-Eulerian
• adaptive downsampling
• cross-attention mechanism
• temporal drift correction
• neural fluid simulation