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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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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Short summary
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.
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