Assessing The Impact of The Homotopy Perturbation Method on Computational Performance in AI Systems

In this study, we evaluated the performance of the Homotopy Perturbation Method (HPM) in ‎different AI application domains through three core metrics: Precision, Efficiency, and Accuracy. ‎The eight AI domains surveyed were as follows: Deep Learning; Reinforcement Learning; ‎Fuzzy Logic AI; Computer Vision; Autonomous Systems; Predictive Analytics; Medical AI; and ‎Optimization Problems. HPM overall performance is constantly higher for Medical AI and ‎Autonomous Systems, and HPM outperforms on precision and accuracy, confirming the ‎robustness because of its insertion in almost all complex, sensitive environments. The balanced ‎outcomes produced by Fuzzy Logic AI and Predictive Analytics further correlate with HPM's ‎ability to deal effectively with uncertain or data-driven models. On the other hand, high ‎performance on Reinforcement Learning and Optimization Problems suggests areas where the ‎rich landscape of HPM might need to be modified or combined with additional computational ‎methods. In general, the results indicate that HPM is a potentially powerful semi-analytical ‎approach for improving the computational efficiency and reliability of several significant AI ‎tasks‎.