This course introduces the theory and practice of hybrid modeling, integrating statistical, conceptual, and physically-based modeling frameworks using Python. Students will explore a range of deterministic and stochastic models, from traditional mechanistic approaches to modern data-driven techniques. Emphasis is placed on understanding model assumptions, structure, calibration, and validation, as well as the implications of model complexity, spatial-temporal scales, and uncertainty. The course culminates in advanced topics such as interpretable AI (XAI) and Bayesian inference, with real-world applications in modeling extreme climate events. Practical implementation in Python will be emphasized throughout to equip students with hands-on experience in hybrid model development and evaluation.

• Develop a comprehensive understanding of different modeling paradigms and their trade-offs (conceptual, empirical, physically-based; deterministic vs stochastic). • Gain proficiency in model development processes including calibration, validation, uncertainty analysis, and sensitivity testing using Python. • Apply hybrid modeling and interpretable AI techniques to complex environmental problems, particularly extreme climate events.

A basic knowledge of, or ability to write, programming code is recommended.

6.0

He, H., & Ma, Y. (Eds.). (2013). Imbalanced learning: Foundations, algorithms, and applications. Wiley-IEEE Press. https://doi.org/10.1002/9781118646106 (available online) Harrell, F. E., Jr. (2015). Regression modeling strategies: With applications to linear models, logistic and ordinal regression, and survival analysis (2nd ed.). Springer. https://doi.org/10.1007/978-3-319-19425-7 (available online) Ibri, S., & Slimane, M. (2022). Probability, stochastic processes and simulation in Python. (available online) Shen, C., Appling, A.P., Gentine, P. et al. Differentiable modelling to unify machine learning and physical models for geosciences. Nat Rev Earth Environ 4, 552–567 (2023). https://doi.org/10.1038/s43017-023-00450-9

Bhattacharyya, S. (2025). Hybrid Computational Intelligent Systems: Modeling, Simulation and Optimization. CRC Press. ISBN: 9781032463292 Butner, J. D., Dogra, P., Chung, C., & others. (2024). Hybridizing mechanistic modeling and deep learning for personalized survival prediction after immune checkpoint inhibitor immunotherapy. npj Systems Biology and Applications, 10, 88. https://doi.org/10.1038/s41540-024-00415-8 Deng, J., Liu, Y., Li, T., Zhang, Y., & Wu, J. (2023). Probabilistic matrix factorization recommendation approach for integrating multiple information sources. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 53(10), 6220–6231. Fakhimi, M., & Mustafee, N. (Eds.). (2024). Hybrid modeling and simulation: Conceptualizations, methods and applications. Springer. ISBN: 3031599985 (available online) Gaur, M., Faldu, K., & Sheth, A. (2021). Semantics of the black-box: Can knowledge graphs help make deep learning systems more interpretable and explainable? IEEE Internet Computing, 25(1), 51–59. Ignacz, G., Bader, L., Beke, A. K., Ghunaim, Y., Shastry, T., Vovusha, H., Carbone, M. R., Ghanem, B., & Szekely, G. (2025). Machine learning for the advancement of membrane science and technology: A critical review. Journal of Membrane Science, 713, 123256. https://doi.org/10.1016/j.memsci.2024.123256 Jiang, S., Shi, N., & Liu, C. (2025). The analysis of artificial intelligence knowledge graphs for online music learning platform under deep learning. Scientific Reports, 15, 16481. https://doi.org/10.1038/s41598-025-01810-9 Pedregosa, F., Varoquaux, G., Gramfort, A., Michel, V., Thirion, B., Grisel, O., Blondel, M., Prettenhofer, P., Weiss, R., Dubourg, V., Vanderplas, J., Passos, A., Cournapeau, D., Brucher, M., Perrot, M., & Duchesnay, É. (2011). Scikit-learn: Machine learning in Python. Journal of Machine Learning Research, 12, 2825–2830.