From Fixed Grids to Moving Particles:A Transferable Latent Operator for Fluid Dynamics

2026-08-14

AI Summary

This study addresses the challenge of zero-shot generalization from Eulerian training data to Lagrangian particle advection. We propose Transferable Implicit Operators, a novel method that learns a unified flow representation while decoupling coordinate decoding to enable zero-shot Lagrangian inference using only Eulerian observations, without requiring additional supervision or adaptation. As the first work achieving zero-shot Eulerian-to-Lagrangian transfer, our approach is validated across five fluid dynamics benchmarks. Experimental results demonstrate that it significantly outperforms existing neural operators in both Eulerian prediction and zero-shot Lagrangian advection tasks. These findings establish a new paradigm for cross-framework fluid modeling, effectively bridging the gap between grid-based and particle-based representations in data-driven scientific computing.

Abstract

Lagrangian modeling is vital to fluid dynamics, as it characterizes particle transport and complements the Eulerian description.However, Lagrangian trajectories are less commonly available than Eulerian fields, while most neural operators are trained and evaluated primarily in the Eulerian representation. This mismatch motivates a new learning problem: can a model trained solely on Eulerian observations generalize zero-shot from Eulerian field prediction to Lagrangian particle rollout, without Lagrangian supervision or task-specific adaptation? To address this problem, we propose the Transferable Latent Operator (TLO), which learns a unified flow representation shared by Eulerian field prediction and Lagrangian particle rollout. TLO decouples latent flow evolution from coordinate-dependent decoding: querying the evolving latent representation at fixed spatial coordinates yields Eulerian fields, whereas querying velocities at particle positions and recursively updating these positions enables Lagrangian rollout. Across five fluid-dynamics benchmarks, TLO consistently outperforms existing neural operators in both Eulerian field prediction and zero-shot Lagrangian rollout, with further gains from limited Lagrangian fine-tuning.

Problem

• Lagrangian particle rollout
• Eulerian field prediction
• zero-shot generalization
• fluid dynamics
• neural operators

Innovation

• Transferable Latent Operator
• Zero-shot Lagrangian Rollout
• Unified Flow Representation
• Decoupled Decoding
• Eulerian-Lagrangian Transfer