Sutterby fluid rheology and electroosmotic phenomena combine the modern electrokinetic transport technologies with the realistic fluid behavior. This enhances predictions that are more accurate, improved designs, and greater performance of a wide array of applications in areas such as process engineering, biotechnology, and so on. In order to capture bioconvective effects, this work models the radiative electroosmotic flow (EOF) of a ternary hybrid nanofluid (TiO₂–Al₂O₃–Fe₃O₄ in a 50:50 propylene glycol–water base) as a non-Newtonian Sutterby fluid which incorporates gyrotactic microorganisms. For sophisticated heat transfer applications, the framework provides a realistic model by taking into account viscous dissipation, chemical processes, nonlinear radiation, porous media, and Joule heating. The objective of this research is to evaluate and improve the heat transfer performance of a ternary hybrid Sutterby nanofluid by modeling and examining its radiative electroosmotic flow, which incorporates bioconvection, porous media, nonlinear radiation, and various thermophysical factors. The governing partial differential equations are reduced via similarity transformations and solved numerically using a sixth-order Runge–Kutta method coupled with the Nachtsheim–Swigert shooting technique. To enhance predictive capability, an artificial neural network (ANN) based on the backpropagated Levenberg–Marquardt algorithm (ANN-BLMS) is implemented. The ANN model exhibits outstanding accuracy, achieving a perfect correlation coefficient (R = 1.0), thereby validating its robustness in modeling nonlinear electroosmotic heat transfer phenomena. Results reveal that for 0 < η < 1.6, the trihybrid PGW fluid velocity increases with magnetic force and then declines, while it consistently rises with Helmholtz, electroosmotic, and Sutterby parameters. Additionally, increasing electroosmotic and Helmholtz parameters tends to suppress heat transfer, while thermal radiation significantly improves it. The Sutterby fluid parameter exhibits a non-monotonic influence on temperature, and microorganism concentration decreases with elevated electroosmotic and Peclet numbers. These findings underscore the utility of ANN as a reliable surrogate modeling tool and highlight the potential of trihybrid nanofluids in applications such as microfluidic drug delivery, advanced cooling technologies, and catalytic systems where precise thermal control and bioconvection are critical.