Generalizability of reservoir computing for flux-driven two-dimensional convection

TL;DR

This paper investigates the ability of echo state networks to generalize in modeling flux-driven two-dimensional turbulent convection, demonstrating successful reproduction of turbulence dynamics and statistical properties across different flux ratios.

Contribution

It introduces a novel application of echo state networks combined with POD and autoencoders to predict complex convection dynamics and tests their generalization capabilities.

Findings

Echo state networks accurately reproduce turbulence dynamics.

The models generalize well to unseen flux ratios.

Both POD and autoencoder inputs effectively capture key features.

Abstract

We explore the generalization properties of an echo state network applied as a reduced dynamical model to predict flux-driven two-dimensional turbulent convection. To this end, we consider a convection domain at fixed height with a variable ratio of buoyancy fluxes at the top and bottom boundaries, which break the top-down symmetry in comparison to the standard Rayleigh-B\'enard case thus leading to highly asymmetric mean and fluctuation profiles across the layer. Our direct numerical simulation model describes a convective boundary layer in a simple way. The data are used to train and test a recurrent neural network in the form of an echo state network. The input to the echo state networks is obtained in two different ways, either by a proper orthogonal decomposition or by a convolutional autoencoder. In both cases, the echo state network reproduces the turbulence dynamics and the statistical properties of the buoyancy flux, and is able to model unseen data records with different flux ratios.