Physics-Informed Machine Learning Models for Reliable Time-Series Forecasting

  • Authors

    • Dr. Andrew Collins Professor, University of Oxford, UK. Author

    DOI:

    https://doi.org/10.67228/3142788X/IJMLPA-2025PII3W2S

    Published 11-05-2025

  • Physics-Informed Machine Learning (PIML), Physics-Informed Neural Networks (PINNs), Time-Series Forecasting, Deep Learning, Scientific Machine Learning, Long Short-Term Memory (LSTM), Transformer Networks, Hybrid Modeling, Differential Equations, Reliable Artificial Intelligence

    Issue

    Vol. 8 No. 2 (2025)

    Section

    Articles

    How to Cite

    [1]
    A. Collins, “Physics-Informed Machine Learning Models for Reliable Time-Series Forecasting”, IJMLPA, vol. 8, no. 2, pp. 01–15, Nov. 2025, doi: 10.67228/3142788X/IJMLPA-2025PII3W2S.

  • Abstract

    Time-series forecasting is considered as one of the cornerstones for intelligent decision-making in various application domains such as renewable energy systems, healthcare, financial markets, climate science, industrial automation and smart transportation. While state-of-the-art deep learning models such as Long Short-Term Memory (LSTM), Gated Recurrent Unit (GRU) and Transformer architectures can produce impressive predictions when trained on a sequence of historical observations, these techniques are primarily data-driven approaches that ignore governing physical principles of dynamic systems. As a consequence, such models can make physically inconsistent predictions, generalise poorly under distributional shifts or use prohibitively large amounts of labeled training data. Common approaches that have been recently introduced to leverage existing domain-specific physical knowledge with data-driven learning to obtain more accurate, robust and interpretable predictions include Physics-Informed Machine Learning (PIML).

  • References

    [1] Raissi, M., Perdikaris, P., & Karniadakis, G. E. (2019). Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics, 378, 686–707. https://doi.org/10.1016/j.jcp.2018.10.045

    [2] Karniadakis, G. E., Kevrekidis, I. G., Lu, L., Perdikaris, P., Wang, S., & Yang, L. (2021). Physics-informed machine learning. Nature Reviews Physics, 3(6), 422–440. https://doi.org/10.1038/s42254-021-00314-5

    [3] Goodfellow, I., Bengio, Y., & Courville, A. (2016). Deep Learning. MIT Press.

    [4] Hochreiter, S., & Schmidhuber, J. (1997). Long short-term memory. Neural Computation, 9(8), 1735–1780.

    [5] Cho, K., van Merriënboer, B., Gulcehre, C., et al. (2014). Learning phrase representations using RNN encoder-decoder for statistical machine translation. Proceedings of EMNLP, 1724–1734.

    [6] Bai, S., Kolter, J. Z., & Koltun, V. (2018). An empirical evaluation of generic convolutional and recurrent networks for sequence modeling. arXiv preprint, arXiv:1803.01271.

    [7] Vaswani, A., Shazeer, N., Parmar, N., et al. (2017). Attention Is All You Need. Advances in Neural Information Processing Systems (NeurIPS), 30.

    [8] Lim, B., Arık, S. Ö., Loeff, N., & Pfister, T. (2021). Temporal Fusion Transformers for interpretable multi-horizon time series forecasting. International Journal of Forecasting, 37(4), 1748–1764.

    [9] Box, G. E. P., Jenkins, G. M., Reinsel, G. C., & Ljung, G. M. (2015). Time Series Analysis: Forecasting and Control (5th ed.). Wiley.

    [10] Brunton, S. L., & Kutz, J. N. (2022). Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control (2nd ed.). Cambridge University Press.

    [11] Willard, J., Jia, X., Xu, S., Steinbach, M., & Kumar, V. (2022). Integrating physics-based modeling with machine learning: A survey. ACM Computing Surveys, 55(4), 1–34.

    [12] Wang, S., Teng, Y., & Perdikaris, P. (2021). Understanding and mitigating gradient pathologies in physics-informed neural networks. SIAM Journal on Scientific Computing, 43(5), A3055–A3081.

    [13] Lu, L., Meng, X., Mao, Z., & Karniadakis, G. E. (2021). DeepXDE: A deep learning library for solving differential equations. SIAM Review, 63(1), 208–228.

    [14] Li, Z., Kovachki, N., Azizzadenesheli, K., et al. (2021). Fourier Neural Operator for parametric partial differential equations. International Conference on Learning Representations (ICLR).

    [15] Pathak, J., Hunt, B., Girvan, M., Lu, Z., & Ott, E. (2018). Model-free prediction of large spatiotemporally chaotic systems from data: A reservoir computing approach. Physical Review Letters, 120(2), 024102.

    [16] Gajula, S. (2024). Cybersecurity risk prediction using graph neural networks. Journal of Information Systems Engineering and Management.

    [17] Gajula, S. (2024). Adaptive zero trust architecture for securing financial microservices. Computer Fraud & Security, 2024(12), 643–655. https://doi.org/10.52710/cfs.845

  • Downloads