This study investigates the role of artificial intelligence in coronary computed tomography angiography analysis, with a focus on the mathematical modeling of stenosed coronary arteries. A detailed comparative analysis is performed between physics-informed neural networks and the finite volume method implemented in the computational software “Analysis System” (ANSYS) environment, both used to solve the governing equations comprising partial and ordinary differential equations that describe the Maxwell viscoelastic behavior of blood and its associated velocity–pressure distributions. Physics-informed neural networks, through their ability to directly embed physical conservation laws into the neural network structure, demonstrate superior capability in producing smooth, accurate, and stable solutions for complex coronary geometries. In contrast, the finite volume method, based on mesh-dependent approximations, shows limitations in addressing strong nonlinearities and geometric irregularities inherent in stenosed arterial flow. The findings reveal that the physics-informed neural network framework outperforms the finite volume method in terms of accuracy, computational efficiency, and adaptability to real-world biomedical complexities. The novelty of this study lies in the first integration of the Maxwell viscoelastic blood model within a physics-informed neural network framework for simulating flow and heat transfer in stenosed coronary arteries, along with a comprehensive validation against the finite volume method. This hybrid approach bridges the gap between artificial intelligence and classical fluid dynamics, offering a robust, mesh-free, and physics-consistent methodology for hemodynamic analysis. Although both methods still face challenges in matching the precision of invasive techniques such as fractional flow reserve, the incorporation of advanced imaging reconstruction and explainable artificial intelligence can further enhance the reliability of non-invasive coronary flow assessment.