On the benefits and limitations of Echo State Networks for turbulent flow prediction

The prediction of turbulent flow by the application of machine learning (ML) algorithms to big data is a concept currently in its infancy which requires further development. It is of special importance if the aim is a prediction that is good in a statistical sense or if the vector fields should be predicted as good as possible. For this purpose, the statistical and deterministic prediction of the unsteady but periodic flow of the von Karman Vortex Street (KVS) was examined using an Echo State Network (ESN) which is well suited for learning from time series due to its recurrent connections. The experimental data of the velocity field of the KVS were collected by Particle Image Velocimetry (PIV). Then, the data were reduced by Proper Orthogonal Decomposition (POD) and the flow was reconstructed by the first hundred most energetic modes. An ESN with 3000 neurons was optimized with respect to its three main hyperparameters to predict the time coefficients of the POD modes. For the deterministic prediction, the aim was to maximize the correct direction of the vertical velocities. The results indicate that the ESN can mimic the periodicity and the unsteadiness of the flow. It is also able to predict the sequence of the upward and downward directed velocities for longer time spans. For the statistical prediction, the similarity of the probability density functions of the vertical velocity fields between the predicted and actual flow was achieved. The leaking rate of the ESN played a key role in the transition from deterministic to statistical predictions.