  In this study, we propose a novel approach, namely the combined Convolutional
Deep Autoencoder Echo State Network (CDAE ESN) model, for the analysis and
forecasting of dynamics and low order statistics in coupled turbulent channel
porous media flows. Such systems find wide applications in industrial settings,
including transpiration cooling and smart interface engineering. However, the
complex geometry of coupled flow systems presents additional challenges for
purely data-driven models. Our results demonstrate that the integration of deep
autoencoder and echo state network techniques enables effective modeling and
prediction of dominant flow behaviors, particularly within the porous domain
exhibiting laminar regimes. To enhance the model s applicability across a
broader range of data domains, we further employ fine-tuning on a dataset
encompassing varying porosities. The achieved average statistics exhibit a
reasonable agreement, underscoring the efficacy of our proposed approach.
