An efficient deep optical flow learning approach for two-dimensional particle image velocimetry

In the particle image velocimetry (PIV) community, velocity fields derived from high-speed camera sensors are invaluable for gaining deeper insight into fluid flow dynamics. However, although current deep learning approaches achieve high accuracy, the most effective models often incur high computational costs, limiting their applicability to PIV estimation. To address this limitation, we propose the recurrent feature pyramid aggregation PIV method (RFPA-PIV), a novel deep learning framework for optical flow estimation designed for two-dimensional (2D) flow fields. RFPA-PIV integrates efficient InceptionNeXt convolutional blocks within a pyramid-based recurrent architecture, reducing computational complexity while maintaining accuracy. Multi-scale features from the pyramid are aggregated and fed into a four-dimensional correlation volume to compute visual similarity. Furthermore, RFPA-PIV was trained on a diverse 2D PIV dataset covering a wide range of flow conditions and evaluated on both synthetic benchmarks and real zebrafish PIV images. Comparative experiments show that RFPA-PIV outperforms existing conventional and deep learning-based methods, achieving accuracy improvements of 80% in cylinder flow, 69% in backstep flow, and 63% in surface quasi-geostrophic flow. It also exhibits strong generalization on real zebrafish PIV data, demonstrating robustness in handling real-world 2D measurement. Compared to other PIV approaches, RFPA-PIV significantly reduces graphics processing unit memory consumption and enables faster inference, effectively balancing model complexity, computational efficiency, and estimation accuracy.