Utilizing neural network modeling to enhance heat transfer behavior in ternary hybrid nanofluid motion over an extending surface

• Rising values of R d and the heat generation parameter led to a noticeable elevation in the temperature of the ternary hybrid nanofluid. • As the thermal Biot number becomes larger, the overall temperature profile diminishes. • Higher values of the magnetic parameter cause the velocity profile to weaken. • As the slip parameter becomes larger, the overall velocity profile weakens. • Using one base fluid containing a uniform mix of three nanoparticle varieties results in superior thermal characteristics. This study examines the laminar two-dimensional flow and heat transfer characteristics of ( A l 2 O 3 - A u - C u O / Propylene Glycol) ternary hybrid nanofluid over a stretching surface, incorporating Cattaneo-Christov non-Fourier heat flux, thermal radiation, magnetic effects, and internal heat generation. The study further evaluates how various nanoparticle geometries sphere, cylindrical, and blade, affect the behavior of the ternary hybrid nanofluid. The governing Partial Differential Equations (PDEs) are transformed into a system of nonlinear Ordinary Differential Equations (ODEs) using similarity variables. A combined Physics‑Informed Neural Network (PINN) and Finite Difference Method (FDM) framework is employed to obtain accurate and stable solutions. The analysis reveals that increasing the magnetic parameter suppresses the velocity field due to enhanced Lorentz drag, while thermal radiation and heat generation parameter significantly elevate the temperature distribution. Nanoparticle geometry also plays a key role, with blade-shaped particles producing the highest thermal enhancement. The results demonstrate the effectiveness of the PINN approach in capturing complex nonlinear behaviors and provide insights useful for advanced thermal management and energy-intensive applications. The thermal relaxation parameter reduces the temperature profile by approximately 24%. Also, increasing the magnetic parameter decreases the velocity by up to 18%.