We apply a physics-informed deep learning method to reconstruct the flow field from sparse and noisy particle tracks, focusing on accurately assimilating the global minimum pressure on a fine-grid domain from very sparse velocity data. The spatial resolution of the velocity data could be much larger than the mesh spacing of the reconstructed flow field. To address this problem, we first quantify the performance of the physics-informed neural network (PINN) model using a series of analytical vortex models. Synthetic particle data are generated using the analytical solutions of the velocities; the PINN model is trained on these sparse particle measurements, and the model then reconstructs the finer-resolution flow field within a fixed domain of interest and obtains the minimum pressure. We also investigate the effects of the reconstruction resolution, particle densities, particle distributions, incomplete measurements, velocity noise, and noise in spatial coordinates. The methodology is applied to a turbulent flow of interacting counterrotating vortices of unequal strength obtained from Large-Eddy Simulation, and the results are discussed.

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• Cavitation
• Large eddy simulations
• Machine learning