Cardiovascular disorders, particularly stenotic arteries, require comprehensive investigation due to their potential to cause life-threatening complications such as stroke and heart attack. This study aims to investigate the significance of Casson nanofluid, which finds applications in targeted drug delivery. The primary objective is to mathematically predict and analyze the impacts of gold and iron oxide nanofluids on blood flow through an artery. The combination of gold and iron oxide nanoparticles in hybrid nanofluids can be utilized in various biological treatments. The study records changes in blood flow patterns to achieve desired temperature, velocity, and pressure changes. The artery is modeled as a cylindrical structure, and governing equations are derived using boundary layer flow fundamentals. These equations are solved using similarity variables and MATLAB software’s bvp4c solver. Artificial neural networks (ANNs) are employed to validate the results by training, testing, and evaluating data. The findings reveal that adjusting the concentration of nanoparticles enhances blood velocity, while reducing the Prandtl number results in subtle trends in temperature curves. Furthermore, increasing nanoparticle concentrations reduces the skin friction coefficient. This work highlights the novelty of integrating deep learning techniques to predict blood flow patterns, paving the way for advancements in the healthcare system.