A lean probabilistic CNN for PIV enabling joint flow and reconstruction uncertainty estimation

Particle Image Velocimetry (PIV) is affected by multiple sources of error arising from imaging conditions, tracer dynamics, and three-dimensional flow effects. While established approaches estimate uncertainty from correlation statistics or particle matching, convolutional neural network (CNN)-based PIV methods typically provide only deterministic displacement fields, limiting quantitative assessment of reconstruction reliability and experimental optimization. In this work, we introduce P-LIMA, a lean probabilistic CNN for PIV that jointly reconstructs the displacement field and a spatially resolved, data-dependent uncertainty estimate. P-LIMA extends the lightweight LIMA architecture by augmenting its output with per-component scale parameters and training the network using a heteroscedastic negative log-likelihood formulation based on Gaussian or Student-t distributions, enabling robust modeling of aleatoric uncertainty. Physically motivated regularization terms on displacement gradients are retained to ensure spatial consistency, while a delayed activation of the probabilistic loss stabilizes training and improves the calibration of hte predicted uncertainty. The method is evaluated on synthetic datasets generated from direct numerical simulations, experimental PIV measurements, and the PIV Challenge 3 (Case B and C) under degraded imaging conditions. Coverage analysis on validation data shows close agreement between empirical and nominal confidence levels, indicating well-calibrated uncertainty estimates. Compared to classical correlation-based approaches, P-LIMA produces uncertainty fields that are more coherent and more strongly correlated with reconstruction errors, while preserving the accuracy of the deterministic baseline model. With approximately 500k parameters and real-time to near-real-time inference on modern GPUs, P-LIMA provides uncertainty estimates without sacrificing computational efficiency.