Hydrology and Earth System Sciences
Hydrology and Earth System Sciences
HESS
Articles | Volume 28, issue 13
Articles | Volume 28, issue 13
https://doi.org/10.5194/hess-28-3051-2024
© Author(s) 2024. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/hess-28-3051-2024
© Author(s) 2024. This work is distributed under
the Creative Commons Attribution 4.0 License.
Articles | Volume 28, issue 13
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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Latest update: 11 Mar 2025
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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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