Echo state networks for modeling turbulent convection

Abstract

Abstract Turbulent Rayleigh-Bénard convection (RBC) is one of the very prominent examples of chaos in fluid dynamics with significant relevance in nature. Meanwhile, Echo State Networks (ESN) are among the most fundamental machine learning algorithms suited for modeling sequential data. The current study conducts reduced order modeling of experimental RBC. The ESN successfully models the flow qualitatively. Even for this highly turbulent flow, it is challenging to distinguish predictions from the ground truth. The statistical convergence of the ESN goes beyond the velocity values and is represented in secondary aspects of the flow dynamics, such as spatial and temporal derivatives and vortices. Finally, ESN’s main hyperparameters show values for best performance in strong relation to the flow dynamics. These findings from both the fluid dynamics and computer science perspective set the ground for future informed design of ESNs to tackle one of the most challenging problems in nature: turbulence.

Keywords

• Echo state networks
• Turbulence
• Rayleigh-Bénard convection
• Reduced order modeling