Articles | Volume 27, issue 12
https://doi.org/10.5194/hess-27-2357-2023
© Author(s) 2023. 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-27-2357-2023
© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
The suitability of differentiable, physics-informed machine learning hydrologic models for ungauged regions and climate change impact assessment
Dapeng Feng
Civil and Environmental Engineering, The Pennsylvania State
University, University Park, PA, USA
Hylke Beck
Physical Science and Engineering, King Abdullah University of
Science and Technology, Thuwal, Saudi Arabia
Kathryn Lawson
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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- Catchment features-based interpretation of performance of the conceptual hydrological and deep learning models using large sample hydrologic data D. Sourya et al. https://doi.org/10.1016/j.jhydrol.2025.134270
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- Challenges and opportunities of ML and explainable AI in large-sample hydrology L. Slater et al. https://doi.org/10.1098/rsta.2024.0287
- Distinct hydrologic response patterns and trends worldwide revealed by physics-embedded learning H. Ji et al. https://doi.org/10.1038/s41467-025-64367-1
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- Runoff prediction in gauged and ungauged basins using Transformer-XAJ model H. Yin et al. https://doi.org/10.1016/j.jhydrol.2025.133954
- Identification of Time-Varying Conceptual Hydrological Model Parameters with Differentiable Parameter Learning X. Lian et al. https://doi.org/10.3390/w16060896
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- Revisit hydrological modeling in ungauged catchments comparing regionalization, satellite observations, and machine learning approaches R. Dasgupta et al. https://doi.org/10.1016/j.hydres.2023.11.001
- Exploring the feasibility of Support Vector Machine for short-term hydrological forecasting in South Tyrol: challenges and prospects D. Dalla Torre et al. https://doi.org/10.1007/s42452-024-05819-z
- Combining physical models and machine learning for enhanced soil moisture estimation M. Li et al. https://doi.org/10.1016/j.compag.2026.111480
- From Gauged to Ungauged: Using Catchment Morphology to Guide the Transfer of Physics‐Informed Neural Network Discharge Predictions M. Khan et al. https://doi.org/10.1002/hyp.70579
- Predicting annual peak daily streamflow in natural basins using quantile regression forests K. Kim et al. https://doi.org/10.1016/j.jhydrol.2025.133233
- A Surrogate Model for Shallow Water Equations Solvers with Deep Learning Y. Song et al. https://doi.org/10.1061/JHEND8.HYENG-13190
- Utilizing CMIP6-SSP scenarios with the VIC model to enhance agricultural and ecological water consumption predictions and deficit assessments in arid regions Q. Bao et al. https://doi.org/10.1016/j.compag.2025.110083
- Deep dive into hydrologic simulations at global scale: harnessing the power of deep learning and physics-informed differentiable models (δHBV-globe1.0-hydroDL) D. Feng et al. https://doi.org/10.5194/gmd-17-7181-2024
- Bridging process-based simulation and deep learning: A location-aware framework for quantifying water diversion impacts on groundwater recovery Y. Song et al. https://doi.org/10.1016/j.ejrh.2026.103480
- Advancing streamflow prediction in data-scarce regions through vegetation-constrained distributed hybrid ecohydrological models L. Zhong et al. https://doi.org/10.1016/j.jhydrol.2024.132165
- Incorporating artificial intelligence into the future of stormwater management M. Rahman et al. https://doi.org/10.1007/s42452-026-08488-2
- AI-enabled predictive pipelines for early warning of agricultural pests, plant diseases, and drought M. Sarker https://doi.org/10.1016/j.atech.2026.101968
- Advancing Hydrology through Machine Learning: Insights, Challenges, and Future Directions Using the CAMELS, Caravan, GRDC, CHIRPS, PERSIANN, NLDAS, GLDAS, and GRACE Datasets F. Hasan et al. https://doi.org/10.3390/w16131904
- HydroGRAF: Hybrid discharge reconstruction and basin-aware streamflow forecasting in the Himalayas A. Gul et al. https://doi.org/10.1016/j.jhydrol.2026.135479
- Multi-layer grid-scale soil moisture estimation using spatiotemporal deep learning methods with physical constraints T. Zhang et al. https://doi.org/10.1016/j.jhydrol.2025.133086
- High-resolution remote sensing-driven water management in semi-arid basins: A CNN-Attention-SWAT fusion framework for the Fen River J. Liu et al. https://doi.org/10.1016/j.srs.2025.100333
- A data-driven framework for monthly hydrological modelling in regulated basins: application to the Jucar Hydrographic Confederation A. Garcia-Monteagudo et al. https://doi.org/10.1007/s40899-026-01362-4
- Probing the limit of hydrologic predictability with the Transformer network J. Liu et al. https://doi.org/10.1016/j.jhydrol.2024.131389
- Physics-informed neural networks for predicting sediment transport in pressurized pipe flows R. Tipu et al. https://doi.org/10.1007/s12665-025-12295-0
- Enhancing flood prediction through physics-driven typhoon feature engineering and machine learning Z. Zhang et al. https://doi.org/10.1371/journal.pone.0346237
- Assessing the adequacy of traditional hydrological models for climate change impact studies: a case for long short-term memory (LSTM) neural networks J. Martel et al. https://doi.org/10.5194/hess-29-2811-2025
- δHT4P: A differentiable physical modeling framework for thermal evolution of permafrost L. Gou & W. Likos https://doi.org/10.1016/j.compgeo.2026.108132
- Evaluating the Hydrological Applicability of Satellite Precipitation Products Using a Differentiable, Physics-Based Hydrological Model in the Xiangjiang River Basin, China S. Yan et al. https://doi.org/10.3390/rs18010137
- Advancing Sub-Seasonal to Seasonal Streamflow Forecasting in Canada: A Review of Conventional and Emerging Approaches for Operational Applications D. Nguyen et al. https://doi.org/10.1016/j.rineng.2025.106345
- Reconstruction of the Vertical Distribution of Suspended Sediment Using Support Vector Machines F. Zhang et al. https://doi.org/10.3390/jmse14080695
- Enhancing the performance of runoff prediction in data-scarce hydrological domains using advanced transfer learning S. Chen et al. https://doi.org/10.1016/j.resenv.2024.100177
- A flexible, differentiable framework for neural-enhanced hydrological modeling: Design, implementation, and applications with HydroModels.jl X. Jing et al. https://doi.org/10.1016/j.envsoft.2025.106802
- Assessing Climate and Watershed Controls on Rain-on-Snow Runoff Using XGBoost-SHAP Explainable AI (XAI) Y. Aryal https://doi.org/10.3390/geosciences15120467
- Machine learning paradigms in natural and engineered water systems: From proof-of-concept to trustworthy deployment R. Ma et al. https://doi.org/10.1016/j.watres.2026.125932
- Physics-informed deep learning reveals climate-driven snowpack decline and threatens ecological water availability in a Californian snow-fed catchment S. Maharjan et al. https://doi.org/10.1016/j.ecoinf.2025.103526
- Applications of physics-informed neural networks in geosciences: From basic seismology to comprehensive environmental studies M. Habib et al. https://doi.org/10.1515/geo-2025-0853
- Technical Note: The divide and measure nonconformity – how metrics can mislead when we evaluate on different data partitions D. Klotz et al. https://doi.org/10.5194/hess-28-3665-2024
- Various Indices of Meteorological and Hydrological Drought in the Warta Basin in Poland J. Wicher-Dysarz et al. https://doi.org/10.3390/w17213035
- Is smart sampling worth it? Impact of training data selection on the performance of LSTMs in streamflow prediction B. Heudorfer & R. Loritz https://doi.org/10.2166/nh.2026.119
- Coupling SWAT+ with LSTM for enhanced and interpretable streamflow estimation in arid and semi-arid watersheds, a case study of the Tagus Headwaters River Basin, Spain S. Asadi et al. https://doi.org/10.1016/j.envsoft.2025.106360
- Daily runoff prediction for ungauged basins: Optimization of model transfer and selection of donor basins X. Song et al. https://doi.org/10.1007/s11430-024-1630-7
- Deep Learning-Based Monthly Runoff Simulation in Changing Environments: Enhancing Accuracy by Reducing Data Redundancy S. Liu et al. https://doi.org/10.1007/s11269-026-04680-6
- HieraBoost-Q: interpretable karst discharge prediction from multi-site electrical conductivity with SHAP-based mechanism insights Y. Zhu et al. https://doi.org/10.1016/j.jhydrol.2026.135153
Saved (final revised paper)
Latest update: 05 Jun 2026
Short summary
Powerful hybrid models (called δ or delta models) embrace the fundamental learning capability of AI and can also explain the physical processes. Here we test their performance when applied to regions not in the training data. δ models rivaled the accuracy of state-of-the-art AI models under the data-dense scenario and even surpassed them for the data-sparse one. They generalize well due to the physical structure included. δ models could be ideal candidates for global hydrologic assessment.
Powerful hybrid models (called δ or delta models) embrace the fundamental learning capability...