让神经网络从流场预测扩展到粒子轨迹推演，无需额外训练。
From Fixed Grids to Moving Particles:A Transferable Latent Operator for Fluid Dynamics
- 用统一潜空间建模流体，分离潜变量演化与坐标解码。
- 在5个基准上零样本预测粒子轨迹，精度超现有方法。
- 适合需要跨流场与粒子模拟的科研和工程应用。
拉格朗日建模对流体动力学至关重要，能刻画粒子输运，补充欧拉表示。然而，拉格朗日轨迹数据远少于欧拉场数据，而多数神经算子主要在欧拉框架下训练和评估。这一差距催生新问题：能否仅基于欧拉观测训练模型，实现零样本从欧拉场预测到拉格朗日粒子滚动的泛化，且无需拉格朗日监督或任务特化调整？为此，我们提出可迁移潜空间算子（TLO），学习一个同时支持欧拉场预测与拉格朗日粒子滚动的统一流体表示。TLO将潜流演化与坐标相关解码解耦：在固定空间坐标查询潜变量得欧拉场；在粒子位置查询速度并递归更新位置，实现拉格朗日滚动。在五个流体动力学基准上，TLO在欧拉场预测和零样本拉格朗日滚动中均持续优于现有神经算子，有限拉格朗日微调后性能进一步提升。
原文摘要 · Abstract (English)
Lagrangian modeling is vital to fluid dynamics, as it characterizes particle transport and complements the Eulerian representation. 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.
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