Numerical Assessment of a Nonintrusive Surrogate Model Based on Recurrent Neural Networks and Proper Orthogonal Decomposition: Rayleigh–Bénard Convection

Abstract

Recent developments in diagnostic and computing technologies offer to leverage numerous forms of nonintrusive modelling approaches from data where machine learning can be used to build computationally cheap and accurate surrogate models. To this end, we present a nonlinear proper orthogonal decomposition (POD) framework, denoted as NLPOD, to forge a nonintrusive reduced-order model for the Boussinesq equations. In our NLPOD approach, we first employ the POD procedure to obtain a set of global modes to build a linear-fit latent space and utilise an autoencoder network to compress the projection of this latent space through a nonlinear unsupervised mapping of POD coefficients. Then, long short-term memory (LSTM) neural network architecture is utilised to discover temporal patterns in this low-rank manifold. While performing a detailed sensitivity analysis for hyperparameters of the LSTM model, the trade-off between accuracy and efficiency is systematically analysed for solving a canonical Rayleigh–Bénard convection system.