This study numerically investigates heat convection and entropy generation in a hybrid nanofluid (Al2O3–Cu–water) flowing around a cylinder embedded in porous media. An artificial neural network is used for predictive analysis, in which numerical data are generated to train an intelligence algorithm and to optimize the prediction errors. Results show that the heat transfer of the system increases when the Reynolds number, permeability parameter, or volume fraction of nanoparticles increases. However, the functional forms of these dependencies are complex. In particular, increasing the nanoparticle concentration is found to have a nonmonotonic effect on entropy generation. The simulated and predicted data are subjected to particle swarm optimization to produce correlations for the shear stress and Nusselt number. This study demonstrates the capability of artificial intelligence algorithms in predicting the thermohydraulics and thermodynamics of thermal and solutal systems.