<p>This study investigates the production of entropy and thermal transition phenomena in MHD nanoliquid movement via a porous octagonal enclosure with a central obstacle and establishes an ANN model for predicting the average Nusselt number (Nu_avg) based on FEM simulations. The equations governing the flow and thermal transference in steady, incompressible, two-dimensional nanofluid flow were derived using the Darcy–Forchheimer model to include the effect of the porous medium and solved numerically employing the Galerkin finite element method (GFEM). Analysis of grid independence was performed to ensure the accuracy of the computation. Copper nanoparticles mixed with water is used as the working fluid to improve the heat conductivity. To estimate the Nusselt number obtained from the FEM, a feedforward back-propagation ANN employing the Levenberg–Marquardt optimization paradigm was created, trained, and validated using data division for training (70%), validation (15%), and testing (15%). It is found that intensification in thermal transition and thermal conductivity by convection is achieved due to the incorporation of nanoparticles, resulting in a maximum increase of the Nu_avg of 7.7% over the pure liquid. Higher Rayleigh numbers strengthen buoyancy effects and render high-velocity and temperature gradients. The ANN model demonstrated high efficiency in forecasting outcomes, resulting in a nearly perfect correlation coefficient (R) of ≈ 1 and mean squared error (MSE) of 5.59 × 10⁻⁸, indicating strong conformity with the FEM results. This analysis provides valuable insights for the design and optimization of advanced thermal management systems, where efficient heat removal from confined geometries is required. Several practical engineering and technological applications are involved in cooling electronic devices, energy systems, and heat exchangers, as well as renewable energy technologies.</p>