Learning spatiotemporal dynamics in a turbulent flow: A 3D Autoencoded Reservoir Computer approach*

Deep learning has shown the potential to learn the dynamics of chaotic systems and reduced-order models of turbulence. The scalability of deep learning to three dimensional turbulent flows as well as the ability to time-accurately predict their evolution, however, are yet to be investigated. 

We introduce a 3D Convolutional AutoEncoded reservoir computer (CAE-RC) based on Echo State Networks to predict the evolution of a turbulent channel flow that exhibits quasi-relaminarization events. The CAE-RC is composed of (i) a 3D Convolutional Autoencoder, which learns an optimal reduced-order representation of the flow state, and (ii) an Echo State Network, which predicts the time flow evolution in the latent space. The CAE-RC is employed to learn the spatiotemporal dynamics of the Minimal Flow Unit (MFU) in the turbulent regime with a Reynolds number of 3000. The CAE-RC is shown able to perform short-term time-accurate predictions and reproduce the statistics of velocity of the flow.

The proposed architecture opens opportunities for reduced-order modelling and learning of the dynamics of turbulent flows.