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This research introduces the Transferable Latent Operator (TLO), a neural architecture capable of zero-shot generalization from Eulerian field predictions to Lagrangian particle rollouts in fluid dynamics. By decoupling latent flow evolution from coordinate-dependent decoding, TLO addresses a critical data mismatch where trajectory information is often scarce compared to standard grid-based fields. The model demonstrates superior performance across five benchmarks, offering a scalable approach for simulating complex transport phenomena without requiring extensive task-specific adaptation or Lagrangian supervision.
From Fixed Grids to Moving Particles:A Transferable Latent Operator for Fluid Dynamics
arXiv:2608.14120v1 Announce Type: new 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.
Abstract:Lagrangian modeling is vital to fluid dynamics, as it characterizes particle transport and complements the Eulerian this http URL, 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.
Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Graphics (cs.GR)
arXiv:2608.14120 [cs.LG]
(or arXiv:2608.14120v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2608.14120 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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