Xin et al. (2025) A flexible, differentiable framework for neural-enhanced hydrological modeling: Design, implementation, and applications with HydroModels.jl

Identification

• Journal: Environmental Modelling & Software
• Year: 2025
• Date: 2025-11-28
• Authors: Jing Xin, Xue Yang, Jungang Luo, Ganggang Zuo
• DOI: 10.1016/j.envsoft.2025.106802

Research Groups

State Key Laboratory of Water Engineering Ecology and Environment in Arid Area, Xi’an University of Technology, Xi’an, Shaanxi, China

Short Summary

This paper introduces HydroModels.jl, a flexible and differentiable Julia-based framework designed to overcome challenges in integrating deep learning with hydrological models by supporting automatic differentiation and symbolic programming for hybrid modeling applications.

Objective

• To design, implement, and demonstrate a flexible, differentiable framework (HydroModels.jl) that facilitates neural-enhanced hydrological modeling, specifically addressing challenges in automatic differentiation requirements and interface incompatibilities for hybrid models.

Study Configuration

• Spatial Scale: General; applicable across diverse hydrological systems and regions.
• Temporal Scale: General; flexible to accommodate various temporal resolutions depending on the integrated hydrological models.

Methodology and Data

• Models used: HydroModels.jl (a flexible, differentiable framework for integrating hydrological and deep learning models).
• Data sources: Not specified for the framework's development; designed to integrate various hydrological and deep learning model inputs.

Main Results

• A flexible and differentiable framework, HydroModels.jl, was designed and implemented in the Julia programming language.
• The framework utilizes symbolic programming to simplify the development of hydrological models, particularly for hybrid models integrating deep learning.
• It supports automatic differentiation, which is crucial for optimizing complex hybrid models.
• HydroModels.jl effectively addresses interface incompatibilities, enabling seamless integration of deep learning components with process-based hydrological models.
• Its integration capabilities and applicability were demonstrated through two illustrative case studies.

Contributions

• Proposes a novel, flexible, and differentiable framework (HydroModels.jl) specifically tailored for neural-enhanced hydrological modeling.
• Overcomes significant challenges in hybrid modeling related to automatic differentiation requirements and interface incompatibilities.
• Leverages symbolic programming and the Julia language to enhance the ease of hydrological model development and optimization.
• Provides a unified and publicly accessible environment for developing, comparing, and refining both specialized hydrological and hybrid model structures.

Funding

Not specified in the provided text.

Citation

@article{Xin2025flexible,
  author = {Xin, Jing and Yang, Xue and Luo, Jungang and Zuo, Ganggang},
  title = {A flexible, differentiable framework for neural-enhanced hydrological modeling: Design, implementation, and applications with HydroModels.jl},
  journal = {Environmental Modelling & Software},
  year = {2025},
  doi = {10.1016/j.envsoft.2025.106802},
  url = {https://doi.org/10.1016/j.envsoft.2025.106802}
}