On the spatial prediction of the turbulent flow behind an array of cylinders via echo state networks

This study investigates the capabilities of the spatial prediction of the turbulent flow behind an array of seven cylinders via Echo State Networks (ESN). The flow is dominated by five distinct unsteady vortex streets, each with its own characteristics, that interact with each other. The goal is to reconstruct the entire section of the flow field by training the ESN to predict the values based on the available low resolution experimental data from the rest of the flow field. Four scenarios - forward, backward, vertical, and central - of data availability to the ESN have been explored. The ESN is capable of reconstructing realistic flow fields in terms of the shape of the packs of up and downward vortices alongside their correct arrangements behind each cylinder. Furthermore, the variable phase synchronization of the neighboring cylinders has been well preserved. Nevertheless, there are preferable regions that result in better predictions of the rest of the flow when they are available to the network. Prediction of the downstream region is more challenging due to the increased entropy of the flow as the vortices move downstream. Furthermore, the most compact area of the information seems to be the central vortex street, as it produces better predictions with the lowest amount of input grid points. The spatial predictions remain stable over time, unaffected by divergence, and are largely insensitive to variations in network hyperparameters, except incases of very small leaking rates.