Articles | Volume 28, issue 13
https://doi.org/10.5194/hess-28-3051-2024
https://doi.org/10.5194/hess-28-3051-2024
Research article
 | 
15 Jul 2024
Research article |  | 15 Jul 2024

When ancient numerical demons meet physics-informed machine learning: adjoint-based gradients for implicit differentiable modeling

Yalan Song, Wouter J. M. Knoben, Martyn P. Clark, Dapeng Feng, Kathryn Lawson, Kamlesh Sawadekar, and Chaopeng Shen

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Technical note: How many models do we need to simulate hydrologic processes across large geographical domains?
Wouter J. M. Knoben, Ashwin Raman, Gaby J. Gründemann, Mukesh Kumar, Alain Pietroniro, Chaopeng Shen, Yalan Song, Cyril Thébault, Katie van Werkhoven, Andrew W. Wood, and Martyn P. Clark
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2024-279,https://doi.org/10.5194/hess-2024-279, 2024
Revised manuscript under review for HESS
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Subject: Catchment hydrology | Techniques and Approaches: Modelling approaches
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Cited articles

Aboelyazeed, D., Xu, C., Hoffman, F. M., Liu, J., Jones, A. W., Rackauckas, C., Lawson, K., and Shen, C.: A differentiable, physics-informed ecosystem modeling and learning framework for large-scale inverse problems: demonstration with photosynthesis simulations, Biogeosciences, 20, 2671–2692, https://doi.org/10.5194/bg-20-2671-2023, 2023. 
Addor, N., Newman, A. J., Mizukami, N., and Clark, M. P.: Catchment Attributes and MEteorology for Large-Sample studies (CAMELS) version 2.0, NCAR, https://doi.org/10.5065/D6G73C3Q, 2017. 
Aghakouchak, A. and Habib, E.: Application of a Conceptual Hydrologic Model in Teaching Hydrologic Processes, Int. J. Eng. Educ., 26, 963–973, 2010. 
Bandai, T.: Inverse Modeling of Soil Moisture Dynamics: Estimation of Soil Hydraulic Properties and Surface Water Flux, PhD thesis, University of California, Merced, California, USA, 172 pp., https://escholarship.org/uc/item/8gb9m1gm#article_main (last access: 11 July 2024), 2022. 
Beck, H. E., van Dijk, A. I. J. M., de Roo, A., Miralles, D. G., McVicar, T. R., Schellekens, J., and Bruijnzeel, L. A.: Global-scale regionalization of hydrologic model parameters, Water Resour. Res., 52, 3599–3622, https://doi.org/10.1002/2015WR018247, 2016. 
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Differentiable models (DMs) integrate neural networks and physical equations for accuracy, interpretability, and knowledge discovery. We developed an adjoint-based DM for ordinary differential equations (ODEs) for hydrological modeling, reducing distorted fluxes and physical parameters from errors in models that use explicit and operation-splitting schemes. With a better numerical scheme and improved structure, the adjoint-based DM matches or surpasses long short-term memory (LSTM) performance.