Neural optical flow for planar and stereo PIV

Neural optical flow (NOF) offers improved accuracy and robustness over existing OF methods for particle image velocimetry (PIV). Unlike other OF techniques, which rely on discrete displacement fields, NOF parameterizes the physical velocity field using a continuous neural-implicit representation. This formulation enables efficient data assimilation and ensures consistent regularization across views for stereo PIV. The neural-implicit architecture provides significant data compression and supports a space–time formulation, facilitating the analysis of both steady and unsteady flows. NOF incorporates a differentiable, nonlinear image-warping operator that relates particle motion to intensity changes between frames. Discrepancies between the advected intensity field and observed images form the data loss, while soft constraints, such as integrated Navier–Stokes residuals, enhance accuracy and enable direct pressure inference from PIV images. Additionally, mass continuity can be imposed as a hard constraint for both 2D and 3D flows. Results from synthetic planar and stereo PIV datasets, as well as experimental planar data, demonstrate that NOF outperforms state-of-the-art wavelet-based OF, cross-correlation, and selected supervised machine learning methods. Beyond PIV, NOF could be used in conjunction with techniques like background-oriented schlieren, molecular tagging velocimetry, and other advanced measurement systems.