Hu et al. (2026) Beyond prediction accuracy: using differentiable hybrid models as a tool for hydrological knowledge discovery

Identification

• Journal: Journal of Hydrology
• Year: 2026
• Date: 2026-08-02
• Authors: Yuqian Hu, Wenhao Chu, Yuxuan Wang, Chunxiao Zhang, Rongrong Li, Heng Li, Yazhou Qi
• DOI: 10.1016/j.jhydrol.2026.136147

Research Groups

• School of Artificial Intelligence, China University of Geosciences in Beijing
• Chinese Academy of Surveying and Mapping
• Hebei Key Laboratory of Geospatial Digital Twin and Collaborative Optimization, China University of Geosciences Beijing
• Observation and Research Station of Beijing Fangshan Comprehensive Exploration, Ministy of Natural Resources
• Institute of Space and Earth Information Science, The Chinese University of Hong Kong
• Key Laboratory of Virtual Geographic Environment (Ministry of Education of PRC), Nanjing Normal University

Short Summary

This study introduces a closed "diagnosis-extraction-improvement" framework that repurposes differentiable hybrids to identify, correct, and theoretically advance structural deficiencies in traditional process-based hydrological models. The framework successfully identified the temperature- and daylength-based Hamon potential evapotranspiration (PET) formulation as the dominant structural bottleneck at the continental scale.

Objective

• To develop a novel framework for diagnosing and improving traditional process-based hydrological models using differentiable hybrid systems combined with symbolic regression.

Study Configuration

• Spatial Scale: Continental scale, covering 476 diverse CAMELS catchments.
• Temporal Scale: Not specified.

Methodology and Data

• Models used: Differentiable implementation of the EXP-HYDRO model.
• Data sources: CAMELS dataset.

Main Results

• Quantitative Diagnosis: Systematic replacement of individual process modules with neural surrogates identified the temperature- and daylength-based Hamon PET formulation as the dominant structural bottleneck at the continental scale.
• Knowledge Extraction: Symbolic regression successfully distilled the high-performing neural PET surrogate into a parsimonious analytical expression, which recovered >85% of the predictive skill originally provided by the complex neural surrogate.
• Theoretical Improvement: Reintegration of the discovered equation into the original EXP-HYDRO model eliminated long-standing radiation-related systematic biases and restored consistency with the Budyko hypothesis across diverse hydroclimatic regimes.

Contributions

• This study demonstrates that differentiable hybrid systems combined with symbolic regression can serve as a powerful tool for accelerating theory-guided discovery and systematic modernisation of hydrological process representations.
• The framework introduced in this study provides an objective ranking of structural deficiencies, extracts interpretable equations directly from constrained neural surrogates, and proves physical-bias elimination without compensation.

Funding

• This research was funded by the Hebei Key Laboratory of Geospatial Digital Twin and Collaborative Optimization (Grant No. 2023001).
• The work was also supported by the National Natural Science Foundation of China (Grant Nos. 42122001, 41890444).

Citation

@article{Hu2026Beyond,
  author = {Hu, Yuqian and Chu, Wenhao and Wang, Yuxuan and Zhang, Chunxiao and Li, Rongrong and Li, Heng and Qi, Yazhou},
  title = {Beyond prediction accuracy: using differentiable hybrid models as a tool for hydrological knowledge discovery},
  journal = {Journal of Hydrology},
  year = {2026},
  doi = {10.1016/j.jhydrol.2026.136147},
  url = {https://doi.org/10.1016/j.jhydrol.2026.136147}
}