Objective Magnetically influenced bioconvective flow of ternary nanofluid induced by the expansion of curved surface by incorporating thermophoresis, Brownian motion, chemical species, activation energy and motile microbes to elucidate complex thermal fluid transport phenomena. Method ology: The mathematical model describing flow mechanism was formulated in sense of PDEs (partial differential equations), which are converted in ODEs (ordinary differential equations) by employing similar set of variables. Numerical technique by integrating the shooting method and RK-4 approach is employed to obtain the outcomes of study. Afterwards, neuro-computing model is designed to forecast Nusselt number for mono, hybrid and ternary nanoparticles comparatively. Key findings Findings of the analysis indicate that velocity of fluid intensifies by uplifting curvature factor while thermal profile goes down. Thermophoretic and Brownian diffusion factors cause the temperature of the fluid to rise but lower the associated flux. Higher curvature and activation energy factors elevate concentration distribution, whereas microbe density depreciates versus Peclet and bioconvective Lewis numbers. The MSE values obtained during training (2.79e-08, 7.63e-08, and 1.55e-07) demonstrate the model's robustness. Applications It is concluded that heat and mass transportation phenomenon is superior with the induction of ternary nanoparticles as compared to mono and hybrid, giving valuable insights for the design of improved thermal energy storage and bioconvective transference mechanism in engineering and biomedicine utilizations.