Reconstructing complex flows from inertial Lagrangian particle tracks

Particle tracking velocimetry (PTV) is widely used to reconstruct 4D flow states from Lagrangian particle trajectories, a.k.a. "tracks", assuming that particles faithfully follow the flow. However, particles can lag the flow or travel ballistically due to rapid acceleration, large temperature gradients, strong body forces, etc., complicating the interpretation of PTV data. We report a novel method to simultaneously reconstruct unsteady flow states and individual particle properties (e.g., size, density, effective response time, …) from inertial tracks. To do this, we use a neural-implicit particle transport model to predict PTV tracks as a function of estimated flow states and particle properties. The flow states and tracks are parameterized by physics-informed neural networks (or similar). Optimizing an objective loss comprising a PTV data loss, Navier–Stokes residuals, and particle transport residuals yields tracks that match the data, physically-plausible flow states, and estimates of the unknown particle properties. We demonstrate this approach using synthetic tracks of inertial particles carried by laminar and turbulent flows. To the best of our knowledge, we report the first unsteady flow reconstructions from inertial tracks as well as implicit PTV-based particle sizing.