Autoencoded Reservoir Computing for the Spatio-Temporal Prediction of a Turbulent Flow*

The recent development and success in deep learning have demonstrated the ability of neural networks to learn the dynamics of chaotic systems. However, this has mostly been applied to low dimensional systems. The applicability of these deep learning tools to turbulence remains a challenge because of high dimensionality and chaotic dynamics that span multiple spatiotemporal scales.

To tackle this, we develop a reservoir computing (RC) approach coupled with a convolutional autoencoder (CAE) to learn the dynamics of the turbulent flows and time-accurately predict their evolution. The CAE identifies a latent space representation of the flow, whilst the RC, based on Echo State Networks, learns the flow dynamics in the latent space. This framework is tested on the 2D Kolmogorov flow at a regime where it exhibits extreme events. The CAE-RC framework is able to time-accurately predict the evolution of the Kolmogorov flow during an extreme event, whilst correctly reproducing the first and second order statistics of the flow when it is run in an autonomous manner.