  Recent developments in diagnostic and computing technologies offer to
leverage numerous forms of nonintrusive modeling 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 utilize 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 utilized 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 analyzed
for solving a canonical Rayleigh-Benard convection system.
