Neural network reconstruction of fluid flows from tracer-particle displacements

We demonstrate some of the advantages of using artificial neural networks for the post-processing of particle-tracking velocimetry (PTV) data. This study is concerned with the data obtained after particle images have been matched and the obvious outliers have been removed. We show that it is easy to produce simple back-propagation neural networks that can filter the remaining random noise and interpolate between the measurements. They do so by performing a particular form of non-linear global regression that allows them to reconstruct the fluid flow for the entire field covered by the photographs. This is obtained by training these neural networks to learn the fluid dynamics function f that maps the position x of a fluid particle at time t to its position X at time t + Δt. They can do so with a high degree of precision when provided with pairs of matching particle positions (x, X) from only about 2 to 4 pairs of PTV photographs as exemplars. We show that whether they are trained on exact or on noisy data, they learn to interpolate with such a precision that their output is within one pixel of the theoretical output. We demonstrate their accuracy by using them to draw whole streamlines or flow profiles, by iteration from a single starting point.