The Integration of Physics-Informed Machine Learning and Fundamental Physics Theory in the Modeling of Complex Systems
Keywords:
Physics-informed machine learning, Fundamental physics theory, Complex systems, Interpretive case study, Scientific machine learningAbstract
This study aims to explore how researchers and practitioners understand the integration of physics-informed machine learning and fundamental physics theory in the modeling of complex systems. The issue is important because complex system modeling requires not only predictive accuracy, but also physical consistency, interpretability, and scientific trust. This study used a qualitative approach with an interpretive case study design. Data were collected through semi-structured interviews, limited observation, and documentation involving researchers, lecturers, doctoral students, computational model developers, data scientists, and engineers who had experience with physics-based modeling or physics-informed machine learning. The data were analyzed using reflexive thematic analysis to identify patterns of meaning across participant experiences. The findings show four main themes: physical theory as a guide for model construction, negotiation between empirical data and governing equations, trust and interpretability in model validation, and practical barriers in implementation. These findings indicate that physics-informed machine learning is not only a computational technique, but also an epistemic practice shaped by scientific judgment, domain expertise, model assumptions, and interdisciplinary collaboration. The study contributes to the theoretical understanding of scientific machine learning by explaining how physical theory guides interpretation and validation. It also offers practical implications for improving transparent, reliable, and physically consistent modeling practices. Further research should compare the application of physics-informed machine learning across different scientific domains to deepen understanding of its methodological and institutional challenges.
References
Braun, V., & Clarke, V. (2022). Conceptual and design thinking for thematic analysis. Qualitative Psychology, 9(1), 3–26. https://doi.org/10.1037/qup0000196
Braun, V., & Clarke, V. (2025). Reporting guidelines for qualitative research: A values-based approach. Qualitative Research in Psychology. https://doi.org/10.1080/14780887.2024.2382244
Campbell, S., Greenwood, M., Prior, S., Shearer, T., Walkem, K., Young, S., Bywaters, D., & Walker, K. (2020). Purposive sampling: Complex or simple? Research case examples. Journal of Research in Nursing, 25(8), 652–661. https://doi.org/10.1177/1744987120927206
Chen, P., & Zhao, X. (2023). Enhancing the performance of hard-constrained gradient-enhanced physics-informed neural networks using a residual adaptive sampling method. Applied Mathematics and Mechanics, 44, 1063–1084. https://doi.org/10.1007/s10483-023-2994-7
Clarke, V., & Braun, V. (2021). Can I use TA? Should I use TA? Should I not use TA? Comparing reflexive thematic analysis and other pattern-based qualitative analytic approaches. Counselling and Psychotherapy Research, 21(1), 37–47. https://doi.org/10.1002/capr.12360
Cuomo, S., Di Cola, V. S., Giampaolo, F., Rozza, G., Raissi, M., & Piccialli, F. (2022). Scientific machine learning through physics-informed neural networks: Where we are and what’s next. Journal of Scientific Computing, 92, Article 88. https://doi.org/10.1007/s10915-022-01939-z
Eshaghi, M. S., Anitescu, C., Thombre, M., Wang, Y., Zhuang, X., & Rabczuk, T. (2025). Variational physics-informed neural operator for solving partial differential equations. Computer Methods in Applied Mechanics and Engineering, 437, Article 117785. https://doi.org/10.1016/j.cma.2025.117785
Farea, A., Yli-Harja, O., & Emmert-Streib, F. (2024). Understanding physics-informed neural networks: Techniques, applications, trends, and challenges. AI, 5(3), 1534–1557. https://doi.org/10.3390/ai5030074
Farhat, H., Nounou, H., Nounou, M., & Serpedin, E. (2025). Physics-informed machine learning for intelligent gas turbine digital twins: A review. Energies, 18(20), Article 5523. https://doi.org/10.3390/en18205523
Jagtap, A. D., & Karniadakis, G. E. (2020). Extended physics-informed neural networks (XPINNs): A generalized space-time domain decomposition based deep learning framework for nonlinear partial differential equations. Communications in Computational Physics, 28(5), 2002–2041. https://doi.org/10.4208/cicp.OA-2020-0164
Jagtap, A. D., Kharazmi, E., & Karniadakis, G. E. (2020). Conservative physics-informed neural networks on discrete domains for conservation laws: Applications to forward and inverse problems. Computer Methods in Applied Mechanics and Engineering, 365, Article 113028. https://doi.org/10.1016/j.cma.2020.113028
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
LaDonna, K. A., Artino, A. R., Jr., & Balmer, D. F. (2021). Beyond the guise of saturation: Rigor and qualitative interview data. Journal of Graduate Medical Education, 13(5), 607–611. https://doi.org/10.4300/JGME-D-21-00752.1
Li, Z., Zheng, H., Kovachki, N., Jin, D., Chen, H., Liu, B., Azizzadenesheli, K., & Anandkumar, A. (2024). Physics-informed neural operator for learning partial differential equations. ACM/IMS Journal of Data Science, 1(3), Article 14. https://doi.org/10.1145/3648506
Lim, W. M. (2025). What is qualitative research? An overview and guidelines. Australasian Marketing Journal. https://doi.org/10.1177/14413582241264619
Lloyd, N. (2024). To member check or not to member check? An evaluation of member checking in qualitative research. International Journal of Qualitative Methods, 23, 1–12. https://doi.org/10.1177/16094069241301383
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. https://doi.org/10.1137/19M1274067
McClenny, L. D., & Braga-Neto, U. M. (2023). Self-adaptive physics-informed neural networks using a soft attention mechanism. Journal of Computational Physics, 474, Article 111722. https://doi.org/10.1016/j.jcp.2022.111722
McKim, C. (2023). Meaningful member-checking: A structured approach to member-checking. American Journal of Qualitative Research, 7(2), 41–52. https://doi.org/10.29333/ajqr/12973
Wang, S., Sankaran, S., & Perdikaris, P. (2024). Respecting causality for training physics-informed neural networks. Computer Methods in Applied Mechanics and Engineering, 421, Article 116813. https://doi.org/10.1016/j.cma.2024.116813
Wang, S., Wang, H., & Perdikaris, P. (2021). Learning the solution operator of parametric partial differential equations with physics-informed DeepONets. Science Advances, 7(40), Article eabi8605. https://doi.org/10.1126/sciadv.abi8605
Wang, S., Yu, X., & Perdikaris, P. (2022). When and why PINNs fail to train: A neural tangent kernel perspective. Journal of Computational Physics, 449, Article 110768. https://doi.org/10.1016/j.jcp.2021.110768
Willard, J., Jia, X., Xu, S., Steinbach, M., & Kumar, V. (2022). Integrating scientific knowledge with machine learning for engineering and environmental systems. ACM Computing Surveys, 55(4), Article 66. https://doi.org/10.1145/3514228
Wu, C., Zhu, M., Tan, Q., Kartha, Y., & Lu, L. (2023). A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks. Computer Methods in Applied Mechanics and Engineering, 403, Article 115671. https://doi.org/10.1016/j.cma.2022.115671
Yu, J., Lu, L., Meng, X., & Karniadakis, G. E. (2022). Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems. Computer Methods in Applied Mechanics and Engineering, 393, Article 114823. https://doi.org/10.1016/j.cma.2022.114823
Downloads
Published
Issue
Section
License
Copyright (c) 2026 Dewi Puspitasari, Eko Azzahra, Fajar Gunawan (Author)
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
