Physics-Informed Neural Networks Enhanced Particle Tracking Velocimetry: An Example for Turbulent Jet Flow

Particle image velocimetry (PIV) and particle tracking velocimetry (PTV) are important flow visualization technologies for measuring global velocity fields in a nonintrusive manner. However, they are limited by the spatial resolution of the measurement, and they require further postprocessing steps to refine the flow fields. To this end, we employ a deep-learning method, physics-informed neural networks (PINNs), which can integrate the sparse velocity measurements from PIV or PTV with the governing equations of the fluid flow by a neural network. A real experiment, where the tomographic PTV setup is applied to measure the 3-D turbulent jet flow, is considered to evaluate the proposed method. We perform a systematic study based on the experimental data, demonstrating that the PINN-enhanced velocimetry approach can yield super-resolution for the velocity vectors, hence demanding only the order of 100 vectors per snapshot compared to 16 500 vectors at full resolution. In addition, PINNs infer the pressure field without providing any pressure information. The proposed algorithm can be readily implemented with the existing PIV/PTV software, providing a standard method for greatly enhancing experimental data in fluid dynamics.