A learning-based approach for highly accurate measurements of turbulent fluid flows

A new learning-based approach for determining fluid flow velocities and dominant motion patterns from particle images is proposed. It is a local parametric technique based on linear spatio-temporal models, which have previously been obtained by methods of unsupervised learning using proper orthogonal decomposition (POD). The learned motion models, embodied by the first POD modes, capture information about complex relations between neighboring flow vectors in spatio-temporal motion patterns. These motion models ensure the solution of the flow problem to be restricted to the orthogonal space spanned by the POD modes. Additional information about local, dominant flow structures can be gained by the POD modes and related parameters. The method can easily be tuned for different flow applications by choice of training data and, thus, is universally applicable. Beyond its simple implementation, the approach is very efficient, accurate and easily adaptable to all types of flow situations. It is an extension of the optical flow technique proposed by Lucas and Kandade (Proceedings of the 1981 DARPA image understanding workshop, pp 121-130, 1981) in their seminal paper. As such, it can also be applied as a postprocessing step to particle image velocimetry (PIV) measurements and improves the results for all conditions analyzed. The approach was tested on synthetic and real image sequences. For typical use cases of optical flow, such as small image displacements, it was more accurate compared to PIV and all other optical flow techniques tested.