Accurately predicting the future fluid is important to extensive areas, such
as meteorology, oceanology and aerodynamics. However, since the fluid is
usually observed from an Eulerian perspective, its active and intricate
dynamics are seriously obscured and confounded in static grids, bringing horny
challenges to the prediction. This paper introduces a new Lagrangian-guided
paradigm to tackle the tanglesome fluid dynamics. Instead of solely predicting
the future based on Eulerian observations, we propose the Eulerian-Lagrangian
Dual Recurrent Network (EuLagNet), which captures multiscale fluid dynamics by
tracking movements of adaptively sampled key particles on multiple scales and
integrating dynamics information over time. Concretely, a EuLag Block is
presented to communicate the learned Eulerian and Lagrangian features at each
moment and scale, where the motion of tracked particles is inferred from
Eulerian observations and their accumulated dynamics information is
incorporated into Eulerian fields to guide future prediction. Tracking key
particles not only provides a clear and interpretable clue for fluid dynamics
but also makes our model free from modeling complex correlations among massive
grids for better efficiency. Experimentally, EuLagNet excels in three
challenging fluid prediction tasks, covering both 2D and 3D, simulated and
real-world fluids.

通过使用 Euler-Lagrange 双重循环网络（EuLagNet）来追踪自适应采样的关键粒子的运动并整合动力学信息，以指导未来的流体预测，本文提出了一种新的拉格朗日引导范式来处理复杂的流体动力学，实验证明 EuLagNet 在 2D 和 3D、模拟和现实世界流体中的三个挑战性流体预测任务中表现出色。