Optical-Flow-Guided Recursive Prediction-Refinement Neural Network for Particle Image Velocimetry

Accurate in-plane displacement field estimation is a key procedure in planar two-dimensional Particle Image Velocimetry (PIV). In this paper, we propose an end-to-end deep learning-based model, termed Recursive Prediction-Refinement Neural Network (RPR-NN), for PIV post-processing. The proposed model estimates dense displacement fields from a single pair of PIV images using a lightweight recurrent unit that incorporates key principles of conventional optical flow solvers, including coarse-to-fine multi-resolution pyramids, iterative warping-based refinement, and gradient-based optical flow constraints derived from the brightness constancy assumption. Furthermore, a spatial attention mechanism is introduced to emphasize high-confidence features, effectively addressing the inherent sparsity of PIV images. RPR-NN is trained on the publicly available PIVDataset and achieves superior accuracy and computational running-time efficiency compared to representative PIV post-processing methods. Quantitative assessments on synthetic datasets show that the proposed model exhibits robust generalization across diverse out-of-distribution scenarios that span a wide spectrum of particle seeding density, diameter, image noise levels, and particle displacement. Its effectiveness is further validated through challenging experimental PIV measurements across a wide range of flow regimes, including low-speed and hypersonic flows, where non-uniform particle seeding and low signal-to-noise ratios create substantial difficulties for conventional PIV post-processing algorithms.