4D DIH-PTV via Stochastic Particle Advection Velocimetry (SPAV)

Particle tracking velocimetry (PTV) is widely used to measure 4D velocity and pressure fields in fluid dynamics research. Particle localization uncertainty is a key source of error in PTV, especially for single camera defocusing, plenoptic imaging, and digital in-line holography (DIH). To address this, we developed stochastic particle advection velocimetry (SPAV): a statistical data loss term that improves the accuracy of PTV. SPAV is based on an explicit particle advection model that estimates particle positions over time as a function of the velocity field. The model can account for non-ideal effects like Stokes drag in a shock. A statistical data loss that compares tracked and advected particle positions, accounting for arbitrary localization uncertainties, is derived and approximated. We demonstrate our approach using a physics-informed neural network, which simultaneously minimizes the SPAV data loss and a Navier–Stokes physics loss, for both synthetic and experimental DIH-PTV data. The statistical approach significantly improves PTV reconstruction compared to a conventional data loss. Our method can be readily adapted to other data assimilation techniques like state observer or adjoint state methods.