Universal Differential Equations for aquatic sciences: application to forecasting lake thermal stratification
Abstract
Predicting lake thermal dynamics is crucial for lake management, particularly under increasing anthropogenic pressures and climate change. Current methods rely either on physics-based models, which are often complex and difficult to calibrate, or on purely data-driven approaches, which may lack interpretability and physical consistency while offering only short-term predictions. We show how Universal Differential Equations (UDEs), hybrid models that add neural networks to existing, even approximate, physics-based equations, can enhance forecasting. On Lake Créteil (Paris region, France), we build a UDE from minimal physics to predict water temperature at five depths and benchmark it against physics-based and data-driven models. For 7-day forecasting, the UDE is the most accurate, and for long-term prediction it is on par with the physics-based model while best reproducing stratification---all with ∼ 90× fewer parameters than a purely data-driven model. We also provide guidelines on UDE architecture and training, transferable to other aquatic variables and systems.
Related
- Best proximity point results of operator type condensing mappings via measure of noncompactness and application to an infinite system of differential equations in c0 and ℓ1
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- Local Hadamard well-posedness of the 2D primitive equations without thermal diffusion under strict stratification
- Synthetic geometry of differential equations: I. Jets and comonad structure
BibTeX
@misc{metivier2026universal,
title = {{Universal Differential Equations for aquatic sciences: application to forecasting lake thermal stratification}},
author = {David Métivier and Ali Elhishi and Mathieu Le Séac'H and Céline Casenave and Brigitte Vinçon-Leite},
howpublished = {HAL},
year = {2026},
month = nov,
url = {https://hal.science/hal-05853811v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Universal Differential Equations for aquatic sciences: application to forecasting lake thermal stratification
AU - David Métivier
AU - Ali Elhishi
AU - Mathieu Le Séac'H
AU - Céline Casenave
AU - Brigitte Vinçon-Leite
PY - 2026
DA - 2026/11/03
PB - HAL
UR - https://hal.science/hal-05853811v1
AB - Predicting lake thermal dynamics is crucial for lake management, particularly under increasing anthropogenic pressures and climate change. Current methods rely either on physics-based models, which are often complex and difficult to calibrate, or on purely data-driven approaches, which may lack interpretability and physical consistency while offering only short-term predictions. We show how Universal Differential Equations (UDEs), hybrid models that add neural networks to existing, even approximate, physics-based equations, can enhance forecasting. On Lake Créteil (Paris region, France), we build a UDE from minimal physics to predict water temperature at five depths and benchmark it against physics-based and data-driven models. For 7-day forecasting, the UDE is the most accurate, and for long-term prediction it is on par with the physics-based model while best reproducing stratification---all with ∼ 90× fewer parameters than a purely data-driven model. We also provide guidelines on UDE architecture and training, transferable to other aquatic variables and systems.
ER -