Echo State Network for two-dimensional turbulent moist Rayleigh-B\'enard convection

TL;DR

This paper demonstrates that an echo state network can effectively predict the complex dynamics of two-dimensional moist Rayleigh-Bénard convection, capturing key turbulence statistics and phase change interactions.

Contribution

It introduces a novel application of echo state networks to model moist convection dynamics, incorporating POD for data reduction and validating predictions against direct numerical simulations.

Findings

Good agreement with original simulation data

Accurate prediction of low-order turbulence statistics

Captures phase change interactions in convection

Abstract

Recurrent neural networks are machine learning algorithms which are suited well to predict time series. Echo state networks are one specific implementation of such neural networks that can describe the evolution of dynamical systems by supervised machine learning without solving the underlying nonlinear mathematical equations. In this work, we apply an echo state network to approximate the evolution of two-dimensional moist Rayleigh-B\'enard convection and the resulting low-order turbulence statistics. We conduct long-term direct numerical simulations in order to obtain training and test data for the algorithm. Both sets are pre-processed by a Proper Orthogonal Decomposition (POD) using the snapshot method to reduce the amount of data. The training data comprise long time series of the first 150 most energetic POD coefficients. The reservoir is subsequently fed by the data and results in predictions of future flow states. The predictions are thoroughly validated by the data of the original simulation. Our results show good agreement of the low-order statistics. This incorporates also derived statistical moments such as the cloud cover close to the top of the convection layer and the flux of liquid water across the domain. We conclude that our model is capable of learning complex dynamics which is introduced here by the tight interaction of turbulence with the nonlinear thermodynamics of phase changes between vapor and liquid water. Our work opens new ways for the dynamic parametrization of subgrid-scale transport in larger-scale circulation models.