Assimilating sparse 3D-PTV data of a pulsed jet using physics-informed neural networks

Phase-resolved volumetric velocity measurements of a pulsed jet are conducted by means of three-dimensional particle tracking velocimetry (PTV). The resulting scattered and relatively sparse data are densely reconstructed by adopting physics-informed neural networks (PINNs), here regularized by the Navier-Stokes equations. It is shown that the assimilation yields a higher spatial resolution, and the process remains robust, even at low particle densities ( 𝑝𝑝𝑝 < 0.001). This is achieved by enforcing compliance with the governing equations, thus leveraging the spatiotemporal evolution of the measured flow field. The results indicate that the PINN reconstructs unambiguously velocity, vorticity and pressure fields with a level of detail not attainable with conventional methods (binning) or more advanced data assimilation techniques (vortex-in-cell). The results of this article support the findings of Clark di Leoni (2023) suggesting that the PINN methodology is inherently suited to the assimilation of PTV data, in particular under conditions of severe sparsity or during experiments with limited control of seeding concentration.