Dense velocity reconstruction from particle image velocimetry/particle tracking velocimetry using a physics-informed neural network

The velocities measured by particle image velocimetry (PIV) and particle tracking velocimetry (PTV) commonly provide sparse information on flow motions. A dense velocity field with high resolution is indispensable for data visualization and analysis. In the present work, a physics-informed neural network (PINN) is proposed to reconstruct the dense velocity field from sparse experimental data. A PINN is a network-based data assimilation method. Within the PINN, both the velocity and pressure are approximated by minimizing a loss function consisting of the residuals of the data and the Navier–Stokes equations. Therefore, the PINN can not only improve the velocity resolution but also predict the pressure field. The performance of the PINN is investigated using two-dimensional (2D) Taylor's decaying vortices and turbulent channel flow with and without measurement noise. For the case of 2D Taylor's decaying vortices, the activation functions, optimization algorithms, and some parameters of the proposed method are assessed. For the case of turbulent channel flow, the ability of the PINN to reconstruct wall-bounded turbulence is explored. Finally, the PINN is applied to reconstruct dense velocity fields from the experimental tomographic PIV (Tomo-PIV) velocity in the three-dimensional wake flow of a hemisphere. The results indicate that the proposed PINN has great potential for extending the capabilities of PIV/PTV.