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

  • Authors

    • Mohanambal B Assistant Professor, Department of Mathematics, Akshaya College of Engineering and Technology, ‎Kinathukadavu, Coimbatore, Tamil Nadu, India
    • Gomathi. K. Assistant Professor, Department of Computer Science and Engineering, Akshaya College of Engineering and ‎ Technology, Kinathukadavu, Coimbatore, Tamil Nadu, India
    • Kulandaivelu. R. Assistant Professor (S. G), Department of Mathematics, Dr. N.G.P Institute of Technology, Coimbatore, Tamil ‎Nadu, India
    • Mekala. v Professor, Department of Artificial Intelligence and Data Science, Arjun College of Technology, Coimbatore, ‎ Tamil Nadu, India
    • Selvamani. C Professor, Department of Mathematics, Karpagam Academy of Higher Education, Coimbatore, Tamil Nadu, ‎India
    https://doi.org/10.14419/zr181f21

    Received date: June 23, 2025

    Accepted date: July 31, 2025

    Published date: August 8, 2025

  • Homotopy Perturbation Method (HPM); AI Application Domains; Precision; Efficiency; Accuracy; Performance Evaluation; Computational Modeling.

  • Abstract

    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.

  • References

    1. Jain, N., Kulshrestha, S., Sharma, M., Gupta, N., & Gaurang, R. (2024) Topological Methods for Solving Nonlinear Equations in Financial. Commu-nications on Applied Nonlinear Analysis, 31(2),113-117 https://doi.org/10.52783/cana.v31.602.
    2. Abraham, S. J., Maduranga, K. D., Kinnison, J., Carmichael, Z., Hauenstein, J. D., & Scheirer, W. J. (2023). Homopt: A homotopy-based hyperpa-rameter optimization method. arXiv preprint arXiv:2308.03317.
    3. Mayumu, N., Xiaoheng, D., & Bagula, A. (2024) Homotopy-Based Pruning: A Topological Approach to Efficient Neural Networks. Available at SSRN 4931668. https://doi.org/10.2139/ssrn.4931668.
    4. Talaat, M., Tayseer, M., Farahat, M. A., & Song, D. (2024). Artificial intelligence strategies for simulating the integrated energy systems. Artificial In-telligence Review, 57(4), 106. https://doi.org/10.1007/s10462-024-10704-7.
    5. Park, J., Karumanchi, S., & Iagnemma, K. (2015). Homotopy-based divide-and-conquer strategy for optimal trajectory planning via mixed-integer programming. IEEE Transactions on Robotics, 31(5), 1101-1115. https://doi.org/10.1109/TRO.2015.2459373.
    6. Biazar, J., & Ghazvini, H. (2009). Convergence of the homotopy perturbation method for partial differential equations. Nonlinear Analysis: Real World Applications, 10(5), 2633-2640. https://doi.org/10.1016/j.nonrwa.2008.07.002.
    7. Parekh, N., Bhagat, A., Raj, B., Chhabra, R. S., Buttar, H. S., Kaur, G., ... & Tuli, H. S. (2023). Artificial intelligence in diagnosis and management of Huntington’s disease. Beni-Suef University Journal of Basic and Applied Sciences, 12(1), 87. https://doi.org/10.1186/s43088-023-00427-z.
    8. Liu, M., Zhang, H., Xu, Z., & Ding, K. (2024). The fusion of fuzzy theories and natural language processing: A state-of-the-art survey. Applied Soft Computing, 111818. https://doi.org/10.1016/j.asoc.2024.111818.
    9. Jiang, Y., Kiumarsi, B., Fan, J., Chai, T., Li, J., & Lewis, F. L. (2019). Optimal output regulation of linear discrete-time systems with unknown dy-namics using reinforcement learning. IEEE transactions on cybernetics, 50(7), 3147-3156. https://doi.org/10.1109/TCYB.2018.2890046.
    10. Osama Alkhazaleh, (2025) Modification of Homotopy Perturbation method for addressing systems of PDEs, Partial Differential Equations in Applied Mathematics, 13 ,101065. https://doi.org/10.1016/j.padiff.2024.101065.
    11. Alaje, A.I., Olayiwola, M.O., Adedokun, K.A. et al. (2022) Modified homotopy perturbation method and its application to analytical solitons of frac-tional-order Korteweg–de Vries equation. Beni-Suef Univ J Basic Appl Sci 11, 139. https://doi.org/10.1186/s43088-022-00317-w.
    12. Gul, H., Ali, S., Shah, K., Muhammad, S., Sitthiwirattham, T., & Chasreechai, S. (2021). Application of Asymptotic Homotopy Perturbation Method to Fractional Order Partial Differential Equation. Symmetry, 13(11), 2215. https://doi.org/10.3390/sym13112215.
    13. G.M. Moatimid, T.S. Amer (2023), Stability analysis of nonlinear systems using homotopy perturbation and frequency expansion methods, Arch Appl Mech, 93 pp. 1029-1042. https://doi.org/10.1007/s00419-023-02395-3.
    14. Paşca, M. S., Bundău, O., Juratoni, A., & Căruntu, B. (2022). The Least Squares Homotopy Perturbation Method for Systems of Differential Equa-tions with Application to a Blood Flow Model. Mathematics, 10(4), 546. https://doi.org/10.3390/math10040546.
    15. Yu D-N, He J-H, Garcıa AG. (2018), Homotopy perturbation method with an auxiliary parameter for nonlinear oscillators. Journal of Low Frequency Noise, Vibration and Active Control. 38(3-4):1540-1554. https://doi.org/10.1177/1461348418811028.
    16. Cheng Xue et al (2021), Quantum homotopy perturbation method for nonlinear dissipative ordinary differential equations, New J. Phys. 23 123035. https://doi.org/10.1088/1367-2630/ac3eff.
    17. Mamatova, H., Eshkuvatov, Z., & Ismail, S. (2024). Homotopy Perturbation Method for Semi-Bounded Solution of the System of Cauchy-Type Sin-gular Integral Equations of the First Kind. Journal of Advanced Research in Applied Sciences and Engineering Technology, 51(2), 124–137. https://doi.org/10.37934/araset.51.2.124137.
    18. Alaje AI, Olayiwola MO, Adedokun KA, Adedeji JA, Oladapo AO (2022) Modifed homotopy perturbation method and its application to analytical solitons of fractional-order Korteweg–de Vries equation. Beni-Suef Univ J Basic Appl Sci 11:1–17. https://doi.org/10.1186/s43088-022-00317-w.
    19. Marwa Mohamed IsmaeelWSEASGoogle Scholar, Wasan Ajeel Ahmood (2023) Using Homotopy Perturbation and Analysis Methods for Solving Different-dimensions Fractional Analytical Equations, WSEAS Transactions on Systems, 22, 2224-2678. https://doi.org/10.37394/23202.2023.22.69.
    20. Bachir N. Kharrat, George A. Toma, (2020). A Hybrid Homotopy Perturbation Method with Natural Transform to Solve Partial Differential equa-tions. International Journal of Scientific Research in Mathematical and Statistical Sciences, 7(4), 14-19.

  • Downloads

  • How to Cite

    B, M. ., K. , G. ., R. , K., v, M. ., & C, S. . (2025). Assessing The Impact of The Homotopy Perturbation Method on Computational Performance in AI Systems. International Journal of Basic and Applied Sciences, 14(4), 199-203. https://doi.org/10.14419/zr181f21