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.
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.
the Creative Commons Attribution 4.0 License.
Research article
| 
15 Jul 2024
Research article |
| 15 Jul 2024
| 15 Jul 2024
When ancient numerical demons meet physics-informed machine learning: adjoint-based gradients for implicit differentiable modeling
Civil and Environmental Engineering, The Pennsylvania State University, University Park, PA, USA
Wouter J. M. Knoben
Department of Civil Engineering, Schulich School of Engineering, University of Calgary, Calgary, Alberta, Canada
Martyn P. Clark
Department of Civil Engineering, Schulich School of Engineering, University of Calgary, Calgary, Alberta, Canada
Dapeng Feng
Civil and Environmental Engineering, The Pennsylvania State University, University Park, PA, USA
Department of Earth System Science, Stanford University, Stanford, CA, USA
Kathryn Lawson
Civil and Environmental Engineering, The Pennsylvania State University, University Park, PA, USA
Kamlesh Sawadekar
Civil and Environmental Engineering, The Pennsylvania State University, University Park, PA, USA
Civil and Environmental Engineering, The Pennsylvania State University, University Park, PA, USA
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- δHT4P: A differentiable physical modeling framework for thermal evolution of permafrost L. Gou & W. Likos https://doi.org/10.1016/j.compgeo.2026.108132
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- Rapid 2D hydrodynamic flood modeling using deep learning surrogates F. Haces-Garcia et al. https://doi.org/10.1016/j.jhydrol.2024.132561
- When physics gets in the way: an entropy-based evaluation of conceptual constraints in hybrid hydrological models M. Álvarez Chaves et al. https://doi.org/10.5194/hess-30-629-2026
- A hybrid physics–AI approach using universal differential equations with state-dependent neural networks for learnable, regionalizable, spatially distributed hydrological modeling N. Huynh et al. https://doi.org/10.5194/gmd-19-1055-2026
Saved (final revised paper)
Latest update: 13 Aug 2026
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.
Differentiable models (DMs) integrate neural networks and physical equations for accuracy,...
