Application of Upadhyaya transforms with machine learning for predictive and analytical solutions in complex systems
DOI:
https://doi.org/10.65112/tcmis.10023Keywords:
Upadhyaya transforms, inverse Upadhyaya transform, machine learning, chemical sciences, physical sciencesAbstract
The study uses the Upadhyaya transform to find exact solutions of three physical models which include the Atwood machine the Beer--Lambert law and electron motion in electromagnetic fields. The proposed framework demonstrates how exact analytical solutions derived via the Upadhyaya transform can be utilized as physically consistent priors, constraints, and validation references within learning-based models, thereby enhancing interpretability, numerical stability, and reproducibility while reducing dependence on large empirical datasets. The research presents an application-oriented method which connects integral transform theory with contemporary machine learning techniques to simulate and study complex physical and chemical systems.
Downloads
References
[1] A. Mousa, “Application of the Upadhyaya transform to Volterra integral equations of the first kind,” Bulletin of Pure and Applied Sciences Section E: Mathematics & Statistics, vol. 40E, no. 2, pp. 140–148, 2021. https://doi.org/10.5958/2320-3226.2021.00016.3 DOI: https://doi.org/10.5958/2320-3226.2021.00016.3
[2] D. Patil, “Application of integral transform (Laplace and Shehu) in chemical sciences,” SSRN, vol. 88, pp. 437–441, 2022. https://doi.org/10.2139/ssrn.4006213 DOI: https://doi.org/10.2139/ssrn.4006213
[3] S. Kulkarni and P. Mahagaonkar, “Study on motion of an electron in a physical system by using some integral transforms,” Eur. Chem. Bull., vol. 12, no. 8, pp. 967–974, 2023.
[4] D. Thakur and E. A. Kuffi, “Exact solutions of cardiovascular models by using Upadhyaya Transform,” Journal of Kufa for Mathematics and Computer, vol. 11, no. 1, pp. 37–42, 2024. https://doi.org/10.31642/JoKMC/2018/110107 DOI: https://doi.org/10.31642/JoKMC/2018/110107
[5] D. Thakur, P. Raghavendran, T. Gunasekar, P. C. Thakur, B. Krishan, and S. Kumar, “Solving the chemical reaction models with the Upadhyaya Transform,” Orient. J. Chem., vol. 40, no. 3, pp. 767–772, 2024. https://doi.org/10.13005/ojc/400318 DOI: https://doi.org/10.13005/ojc/400318
[6] P. Raghavendran, T. Gunasekar, D. Thakur, P. C. Thakur, and B. Krishan, “Predictive modeling of chemical processes using differential equations and machine learning synergy,” Orient. J. Chem., vol. 41, no. 2, pp. 386–392, 2025. https://doi.org/10.13005/ojc/410206 DOI: https://doi.org/10.13005/ojc/410206
[7] P. Raghavendran, T. Gunasekar, and S. Gochhait, “A new approach for solving fractional differential equations incorporating Ramadan Group Transform and machine learning,” EAI Endorsed Trans IoT, vol. 11, pp. 1–12, 2025. https://doi.org/10.4108/eetiot.7134 DOI: https://doi.org/10.4108/eetiot.7134
[8] H. Jafari, S. Aggarwal, A. Kumar, and S. Bansal, “Anuj Integral Transform to solving Abel’s integral equation of classical mechanics,” Natl. Acad. Sci. Lett., pp. 1–5, 2025. https://doi.org/10.1007/s40009-024-01597-9 DOI: https://doi.org/10.1007/s40009-024-01597-9
[9] P. Beeken, “Atwood’s heavy chain,” Phys. Teach., vol. 49, no. 8, pp. 470–472, 2011. https://doi.org/10.1119/1.3651724 DOI: https://doi.org/10.1119/1.3651724
[10] T. B. Greenslade, Jr., “Atwood’s machine,” Phys. Teach., vol. 29, no. 1, pp. 24–28, 1985. https://doi.org/10.1119/1.2341703 DOI: https://doi.org/10.1119/1.2341703
[11] G. Scholz and F. Scholz, “First-order differential equations in chemistry,” ChemTexts., vol. 1, no. 1, p. 1, 2014. https://doi.org/10.1007/s40828-014-0001-x DOI: https://doi.org/10.1007/s40828-014-0001-x
[12] A. A. Mahmud, “Considerable traveling wave solutions of the generalized Hietarinta-type equation,” International Journal of Mathematics and Computer in Engineering, vol. 3, no. 2, pp. 185–200, 2024. https://doi.org/10.2478/ijmce-2025-0015 DOI: https://doi.org/10.2478/ijmce-2025-0015
[13] A. A. Mahmud, T. Tanriverdi, and K. A. Muhamad, “Exact traveling wave solutions for the (2+1)-dimensional Konopelchenko–Dubrovsky equation using hyperbolic trigonometric function methods,” International Journal of Mathematics and Computer in Engineering, vol. 1, no. 1, pp. 11–24, 2023. https://doi.org/10.2478/ijmce-2023-0002 DOI: https://doi.org/10.2478/ijmce-2023-0002
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2026 Yamini Parthiban, Raghavendran Prabakaran, Dinesh Thakur, Srinivasan Madhumitha
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
All open access articles published in Transactions on Computational Modelling and Intelligent Systems (http://tcmis.org) are distributed under the terms of the CC BY-NC 4.0 license (Creative Commons Attribution Non-Commercial 4.0 International Public License as currently displayed at http://creativecommons.org/licenses/by-nc/4.0/legalcode) which permits unrestricted use, distribution, and reproduction in any medium, for non-commercial purposes, provided the original work is properly cited.
