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

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

doi:https://doi.org/10.5194/hess-28-3051-2024

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

Data sets

A large-sample watershed-scale hydrometeorological dataset for the contiguous USA A. Newman et al. https://doi.org/10.5065/D6MW2F4D

MOD16A2 MODIS/Terra Net Evapotranspiration 8-Day L4 Global 500 m SIN Grid V006 S. Running et al. https://doi.org/10.5067/MODIS/MOD16A2.006

Model code and software

mhpi/HydroDLAdj: v1.0 (v1.0) Y. Song https://doi.org/10.5281/zenodo.11205309

HydroDLAdj Y. Song https://github.com/mhpi/HydroDLAdj

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.