Reconstructing complex flows using neural data assimilation

We report a neural data assimilation (DA) algorithm that can reconstruct turbulent Eulerian flow states in a large spatio-temporal domain from noisy Lagrangian tracks. The tracks are obtained via particle tracking velocimetry (PTV): an essential tool for experimental research on fluid turbulence. In PTV, tracer particles are seeded into a flow, illuminated, imaged, and linked across frames to produce a set of spatially-sparse Lagrangian particle trajectories, a.k.a. “tracks.” DA is frequently used to combine the tracks with equations that govern the flow to accurately reconstruct the velocity field and infer latent fields like pressure or density. Crucially, localization and tracking errors can degrade the performance of PTV, especially when using a single-camera setup as in plenoptic or digital-inline-holography PTV. Moreover, the particles may too heavy, too light, too large, or too abundant to act as ideal tracers, preventing easy access to the flow. Our neural DA algorithm can compensate for large, anisotropic localization errors, tracking errors, and inertial particle transport. We formulate physics losses based on the Navier–Stokes and Maxey–Riley equations. PTV data is embedded in our particle transport model as a hard constraint, and the tracked positions, size, and density of each particle may be estimated as part of the reconstruction. We demonstrate the method using simulated measurements of turbulent flows. Accurate flow states and particle properties are reconstructed from unlabeled PTV data.