The main goal of this work is to examine the effects of magnetohydrodynamics on a three-dimensional Powell-Eyring hybrid dusty nanofluid, especially when a heat source is present. The energy equation is modelled using the effects of heat sources and thermal radiation. Levenberg-Marquard algorithm-based multi-layer perception with feed-forward back-propagation is used to simulate the model numerically. The data was meticulously collected to support the ANN model with long bvp4c, a popular numerical technique. The ANN model’s steps involve preparing the data, establishing the network, training, and assessing it using the mean square error measure. Visual depictions in graphs provide insight into the various physical parameters that affect velocity and temperature, skin friction coefficients, and Nusselt numbers. The temperature of dusty fluids and hybrid dusty nanofluids show acceleration with greater thermal radiation parameters, whereas velocity profiles show a notable decrease. The hybrid nanofluid’s increased thermal conductivity enhances energy harvesting and cooling systems.