Reconstructing velocity and pressure from sparse noisy particle tracks using Physics-Informed Neural Networks

Abstract: Volume-resolving imaging techniques are rapidly advancing progress in experimental fluid mechanics. However, reconstructing the full and structured Eulerian velocity and pressure fields from sparse and noisy particle tracks obtained experimentally remains a significant challenge. We introduce a new method for this reconstruction, based on Physics-Informed Neural Networks (PINNs). The method uses a Neural Network regularized by the Navier-Stokes equations to interpolate the velocity data and simultaneously determine the pressure field. We compare this approach to the state-of-the-art Constrained Cost Minimization method [1]. Using data from direct numerical simulations and various types of synthetically generated particle tracks, we show that PINNs are able to accurately reconstruct both velocity and pressure even in regions with low particle density and small accelerations. PINNs are also robust against increasing the distance between particles and the noise in the measurements, when studied under synthetic and experimental conditions.