Reconstructing wall-bounded turbulent flows from limited PIV measurements using Physics Informed Neural Networks

Turbulent flows are characterized by multiple length and time scales. Laboratory techniques used to acquire velocity field measurements such as Particle Image Velocimetry (PIV) are typically limited in their ability to acquire time-resolved velocity fields. In this work we train a Physics Informed Neural Network (PINN) to estimate the velocity field snapshots between consecutive 2D PIV snapshots. The PINN is defined to take the spatial and temporal coordinates as the input and the two velocity field components (streamwise and wall-normal) are the output. The PDE constraint imposed on the reconstructed flow field is consistent with the Taylor's frozen turbulence hypothesis, which has been used successfully for temporal reconstruction in previous studies. A composite loss function is defined to include the error from the PDE and the deviation from the PIV snapshots. The PINN is trained to minimize this composite loss function. The velocity field can now be reconstructed between the two snapshots at arbitrary spatio-temporal resolution. The errors from these reconstructions are evaluated using PIV-like snapshots from numerical simulations of turbulent channel flow from the Johns Hopkins Turbulence Database (JHTDB).