The present study explores the dynamics of a two-dimensional, incompressible nanofluid flow through a stretching curved sheet within a highly porous medium. The mathematical model is formulated by including external forces such as viscous dissipation, thermal radiation, Ohmic heating, chemical reactions, and activation energy by utilizing a curvilinear coordinate system. The viscosity and thermal conductivity of the nanofluids are examined using the Koo-Kleinstreuer-Li model. The choice of $Al_{2}O_{3}$ and $CuO$ nanoparticles in this model stems from their distinct thermal properties and widespread industrial applicability. By non-dimensionalizing the governing partial differential equations, the physical model is simplified into ordinary differential equations. BVP-5C solver in MATLAB is utilized to numerically solve the obtained coupled non-linear ordinary differential equation. Graphical results are presented to investigate the velocity, temperature, and concentration profiles with entropy generation optimization under the influence of several flow parameters. The artificial neural network backpropagated with Levenberg-Marquardt method (ANN-BLMM) used to study the model. The performance is validated using regression analysis, mean square error and error histogram plots. The outcome illustrates that the velocity and temperature profiles increase with increasing the Forchhiemer parameter. Also, the velocity profile increases with increasing curvature parameter, while, reverse effect is observed for temperature profile. This research augments our comprehension of nanofluid dynamics over curved surfaces, which has implications for engineering applications. The insights gained have the potential to significantly contribute to the advancement of energy-efficient and environmentally sustainable cooling systems in industrial processes.