Coarse-to-fine variational inference with physics-informed deep learning for complex fluid motion estimation

Deep learning models for particle imaging velocimetry (PIV) often suffer from complex, black-box architectures that limit efficiency and real-world generalization. We propose a physics-informed variational framework that explicitly embeds classical fluid principles, like incompressibility, into its multi-scale inference structure. This principled design eliminates the need for complex black-box components and achieves new state-of-the-art accuracy on challenging flows. Crucially, the model shows outstanding generalization, applying directly to riverine data without retraining, defining a new path for robust and physically consistent flow measurement.