Data Assimilation of Lagrangian Particle Tracks for Calculation of Flow Parameters Using Physics-Informed Machine Learning

We present a machine learning algorithm for the reconstruction of the flow field from Lagrangian particle tracks. The algorithm is based on a B-spline approximation of the flow field with smooth derivatives. It is possible to restore both the velocity and the pressure fields in the computational domain. Assimilation of experimental data in fluid mechanics is needed to restore the missing details of an experiment using physical constraints. Experimental studies of complex nonstationary flows using three-dimensional whole-field optical methods based on Lagrangian particle tracking with spatial and temporal resolution exceeding the characteristics of currently used methods, while spending less computing resources on data processing, are of great interest for researchers. The results of such measurements in the form of tens of thousands of tracer particle tracks can be used for further analysis of the dynamics of the velocity, acceleration, and pressure fields in flows, as well as the Reynolds stress tensor, which allows validating the velocity and pressure distributions in eddy-resolving nonstationary three-dimensional simulations.