Cross-Disciplinary Modelling of Intelligent Systems Using Advanced Numerical Methods and Adaptive Algorithmic Design
DOI:
https://doi.org/10.63503/j.ijcma.2025.197Keywords:
Cross-Disciplinary Modelling, Intelligent Systems, Numerical Methods, Physics-Informed Neural Networks, Adaptive Algorithms, Dynamical Systems, Multi-Scale Modelling, Computational ScienceAbstract
The scientific challenge of modeling non-disciplinary complexity concerns not only the intelligent systems of the present such as pandemic forecasting or financial predicting; the problem of complex models is universal. These systems are noted as high-dimensional, multi-scale and non-stationary behavior, which could not be modeled proceeding with conventional and siloed approaches. Thus, it demands an integrated system that will utilize the resources of various fields of mathematics to their advantage. The paper presents a transdisciplinary modelling system, which is a synergic reciprocal combination of sophisticated numerical techniques and adaptive algorithm-based design. We no longer see complex phenomena in the world as problems of physics, biology, or finance but as universal dynamical systems, to be solved. Our idea is based on the hybrid approach, where we use Physics-Informed Neural Networks (PINNs) to directly incorporate governing laws into learning systems, yet use an adaptive solver to estimate dynamic parameters. We demonstrate with multi-scenario validation that this general framework is far superior to monolithic models in accuracy, robustness, as well as predictive capability and exists in a wide range of applications, such as in epidemiology and in computational finance. It is a major advance in a direction towards consilience in computational science and offers a general roadmap towards the construction of next-generation intelligent systems that are physically consistent and data-sensitive.
References
[1] C. Fan, F. Xiao, C. Yan, C. Liu, Z. Li, and J. Wang, “A novel methodology to explain and evaluate data-driven building energy performance models based on interpretable machine learning,” Applied Energy, vol. 235, pp. 1551–1560, 2019, doi: 10.1016/j.apenergy.2018.11.081.
[2] P. Rajendra and V. Brahmajirao, “Modeling of dynamical systems through deep learning,” Biophysical Reviews, vol. 12, no. 6, pp. 1311–1320, 2020, doi: 10.1007/s12551-020-00776-4.
[3] G. E. Karniadakis, I. G. Kevrekidis, L. Lu, P. Perdikaris, S. Wang, and L. Yang, “Physics-informed machine learning,” Nature Reviews Physics, vol. 3, no. 6, pp. 422–440, 2021, doi: 10.1038/s42254-021-00314-5.
[4] A. Pesaranghader, H. L. Viktor, and E. Paquet, “McDiarmid drift detection methods for evolving data streams,” in Proc. Int. Joint Conf. Neural Networks (IJCNN), Jul. 2018, pp. 1–9, doi: 10.1109/IJCNN.2018.8489260.
[5] V. S. Spelmen and R. Porkodi, “A review on handling imbalanced data,” in Proc. Int. Conf. Current Trends Towards Converging Technologies (ICCTCT), Mar. 2018, pp. 1–11, doi: 10.1109/ICCTCT.2018.8551020.
[6] H. Najadat, O. Altiti, A. A. Aqouleh, and M. Younes, “Credit card fraud detection based on machine and deep learning,” in Proc. 11th Int. Conf. Information and Communication Systems (ICICS), Apr. 2020, pp. 204–208, doi: 10.1109/ICICS49469.2020.239524.
[7] J. Nordström, K. Forsberg, C. Adamsson, and P. Eliasson, “Finite volume methods, unstructured meshes and strict stability for hyperbolic problems,” Applied Numerical Mathematics, vol. 45, no. 4, pp. 453–473, 2003, doi: 10.1016/S0168-9274(02)00239-8.
[8] S. M. Anwar, M. Majid, A. Qayyum, M. Awais, M. Alnowami, and M. K. Khan, “Medical image analysis using convolutional neural networks: A review,” Journal of Medical Systems, vol. 42, no. 11, Art. no. 226, 2018, doi: 10.1007/s10916-018-1088-1.
[9] H. J. Bungartz, F. Lindner, B. Gatzhammer, M. Mehl, K. Scheufele, A. Shukaev, and B. Uekermann, “preCICE: A fully parallel library for multi-physics surface coupling,” Computers & Fluids, vol. 141, pp. 250–258, 2016, doi: 10.1016/j.compfluid.2016.04.003.
[10] S. Cai, Z. Mao, Z. Wang, M. Yin, and G. E. Karniadakis, “Physics-informed neural networks (PINNs) for fluid mechanics: A review,” Acta Mechanica Sinica, vol. 37, no. 12, pp. 1727–1738, 2021, doi: 10.1007/s10409-021-01148-1.
[11] L. L. Minku, “Transfer learning in non-stationary environments,” in Learning from Data Streams in Evolving Environments: Methods and Applications. Cham, Switzerland: Springer, 2018, pp. 13–37, doi: 10.1007/978-3-319-89803-2_2.
[12] M. Altalhan, A. Algarni, and M. T. H. Alouane, “Imbalanced data problem in machine learning: A review,” IEEE Access, early access, 2025, doi: 10.1109/ACCESS.2025.3531662.
[13] M. W. Hofbaur and B. C. Williams, “Hybrid estimation of complex systems,” IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), vol. 34, no. 5, pp. 2178–2191, Oct. 2004, doi: 10.1109/TSMCB.2004.835009.
[14] L. Ho and P. Goethals, “Machine learning applications in river research: Trends, opportunities and challenges,” Methods in Ecology and Evolution, vol. 13, no. 11, pp. 2603–2621, 2022, doi: 10.1111/2041-210X.13992.
[15] C. N. Kamath, S. S. Bukhari, and A. Dengel, “Comparative study between traditional machine learning and deep learning approaches for text classification,” in Proc. ACM Symp. Document Engineering, Aug. 2018, pp. 1–11, doi: 10.1145/3209280.3209526.
[16] Z. Xu and J. H. Saleh, “Machine learning for reliability engineering and safety applications: Review of current status and future opportunities,” Reliability Engineering & System Safety, vol. 211, Art. no. 107530, 2021, doi: 10.1016/j.ress.2021.107530.
