Near-wall flow recovery from particle image velocimetry using physics-informed neural network

A physics-informed neural network is employed to reconstruct near-wall flow fields from particle image velocimetry (PIV) data in regions where direct measurements are inaccessible. Experiments were conducted in a vertical square duct, and four datasets were prepared with mean velocity components and Reynolds stresses measured at the duct's center plane for Reynolds numbers in the range Re=2.1×104 to 3.2×104. The Reynolds-averaged Navier–Stokes equations were incorporated in the training as physical constraints, and a two-step training strategy was introduced to address closure limitations in near-wall region with insufficient prior knowledge. In the first stage, the model was trained within the PIV domain to denoise the flow data and reconstruct pressure field through data assimilation, producing results consistent with Darcy friction coefficients at each Re. The second stage incorporated additional physical constraints, including force balance and a simplified turbulence-closure approximation, to recover the near-wall flow behavior. The final model produced velocity profiles consistent with turbulent boundary layer theory, capturing the linear viscous sublayer and the onset of the logarithmic region. The reconstructed Reynolds stresses effectively captured the strong near-wall anisotropy reported in previous studies, exhibiting peak approximately eight times larger in the streamwise direction than in the wall-normal direction. Comparisons with models trained without Reynolds stress regularization confirmed that this constraint contributes to improved Reynolds stress prediction.