Extracting information on fluid motion directly from images is challenging.
Fluid flow represents a complex dynamic system governed by the Navier-Stokes
equations. General optical flow methods are typically designed for rigid body
motion, and thus struggle if applied to fluid motion estimation directly.
Further, optical flow methods only focus on two consecutive frames without
utilising historical temporal information, while the fluid motion (velocity
field) can be considered a continuous trajectory constrained by time-dependent
partial differential equations (PDEs). This discrepancy has the potential to
induce physically inconsistent estimations. Here we propose an unsupervised
learning based prediction-correction scheme for fluid flow estimation. An
estimate is first given by a PDE-constrained optical flow predictor, which is
then refined by a physical based corrector. The proposed approach outperforms
optical flow methods and shows competitive results compared to existing
supervised learning based methods on a benchmark dataset. Furthermore, the
proposed approach can generalize to complex real-world fluid scenarios where
ground truth information is effectively unknowable. Finally, experiments
demonstrate that the physical corrector can refine flow estimates by mimicking
the operator splitting method commonly utilised in fluid dynamical simulation.

本文提出一种基于无监督学习的预测 - 校正方案，通过 PDE 约束的光学流预测器给出速度场的估计，并通过基于物理的校正器进行精细化处理，取得了比光学流方法更好的效果，在基准数据集上表现出与现有监督学习方法具有竞争力的结果。