  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.
