<p>This paper utilizes a mathematical model of a ternary hybrid nanofluid (Al₂O₃–graphene–CNT/water) flow over a rotating disk and presents the application of soft computing algorithms for assessing heat transfer. The novelty of this research lies in the parametric aspects of ternary hybrid nanofluid flow and heat transfer over a spinning disk, taking into account the effects of buoyancy force, thermal radiation, and Hall effects. Examples of rotating disk system applications include power generation, geothermal extraction, gears, computer storage technologies, rotor–stator configurations, gas turbine engines, brakes, and flywheels. Transformations are used to transform the partial differential equations to ordinary differential equations, and then, numerical simulations are performed using the “bvp4c method” in MATLAB software. Also, the dataset has been quantitatively constructed for the soft computational approaches (artificial neural network and fuzzy particle swarm optimization), and it is used to predict the Nusselt number values precisely. After finding the results, it is seen that with the increment in value of parameter Rd, the Nusselt number increases from 273.26% (when <i>m</i> = 0.1) to 277.99% (when <i>m</i> = 0.9). It is examined that the THNF flow has a higher radial and azimuthal velocity for assisting flow and has a larger thermal profile for opposing flow. From the findings, it is seen that the highest value of the correlation coefficient using ANN and FPSO is 0.999999088, while the lowest value of MSE using both is 0.000000202346, signifying the prediction with high precision.</p>