AI 中文总结
针对欧拉与拉格朗日流体动力学表示的不匹配问题，提出可迁移潜算子TLO，在五个基准测试中于两类任务均优于现有神经算子，经微调后性能进一步提升。
AI 中文摘要
拉格朗日建模对流体动力学至关重要，因为它可表征粒子输运并补充欧拉方法。然而，拉格朗日轨迹的获取不如欧拉场常见，且多数神经算子的训练与评估主要基于欧拉表示。这种不匹配催生了新的学习问题：仅在欧拉观测上训练的模型，能否在无拉格朗日监督、无任务特定适配的情况下，零样本泛化到从欧拉场预测到拉格朗日粒子演化的任务？为解决该问题，我们提出可迁移潜算子（Transferable Latent Operator, TLO），其学习欧拉场预测与拉格朗日粒子演化共享的统一流表示。TLO将潜流演化与依赖坐标的解码解耦：在固定空间坐标查询演化的潜表示可得到欧拉场，而在粒子位置查询速度并递归更新这些位置可实现拉格朗日演化。在五个流体动力学基准测试中，TLO在欧拉场预测与零样本拉格朗日演化任务上均持续优于现有神经算子，且经有限拉格朗日微调后性能进一步提升。
英文摘要
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.
Comments8 pages, 5 figures, preprint paper
