In this work, we present the findings of the experimental study conducted in a rectangular duct at sonic and supersonic Mach numbers using passive control in the form of semi-circular ribs. Tests are conducted at sonic Mach number and four supersonic Mach numbers. The supersonic Mach numbers of the study are 1.5, 1.8, 2.2, and 2.5. The flow from the nozzles is discharged into the enlarged duct. The ribs are placed at 28 mm (1D), 56 mm (2D), 84 mm (3D), and 112 mm (4D) from the base to find the effect of the control mechanism on the flow field and the base pressure. The ribs of 6, 8, and 10 mm diameter are used to control the base pressure and ultimately the base drag. At Mach 2.2 and 2.5, control is not effective because the nozzles are over-expanded. These results reiterate the findings from the literature that the control is effective whether passive or active when nozzles flow under the influence of a favorable pressure gradient. The same is evident from the results at Mach 1.5 and 1.8. The NPRs at these Mach numbers are such that nozzles are under, correctly, and under expanded. When nozzles are operated for under expanded case, the control results in an increase in the base pressure when passive control is employed. These highly complex data are predicted using a single-layered neural network and a deep-layer neural network to save time and make it cost-effective, which shows that the data can be predicted with an accuracy of 0.88–0.99. The proposed models can predict the highly sensitive pressure terms for aerodynamic flows.