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<p>Physics-embedded machine learning (PeML) models integrate process-based representations with machine learning (ML) components to improve hydrological predictions. Despite their growing adoption, the relative contribution of each component, namely the process-based structure, ML capacity, and coupling interface, remains unclear. To address this, we constructed PeML models by pairing physics-aware recurrent neural networks (PRNNs), derived from four conceptual hydrological models (EXP-HYDRO, HBV, FLEX, and WBM), with a 1D convolutional neural network (1D-CNN) and tested two coupling strategies. Hybrid I inputs both simulated streamflow and meteorological forcings into the 1D-CNN, whereas Hybrid II uses only simulated streamflow. All models were evaluated across 500 basins from the CAMELS-US dataset. Results indicate that PeML models with Hybrid I coupling consistently outperform both standalone PRNNs and the purely data-driven 1D-CNN, with median NSE and KGE above 0.60. Hybrid II models show more variable performance depending on the embedded conceptual model. A systematic sensitivity analysis within the tested architectural configurations shows that the complexity of the 1D-CNN is the dominant factor driving PeML performance, whereas the choice of conceptual model and the input interface have smaller effects. These findings highlight that process-based models provide useful inductive biases, but the design and expressiveness of the ML component primarily determine predictive skill. Although the study offers valuable insights into the relative contribution of each PeML component, its scope, limited to four conceptual models, non-anthropized basins, and a single ML architecture, constrains the generalization of its conclusions. These limitations point toward future investigations that explore alternative PeML designs and more diverse hydrological conditions.</p>

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Key drivers of physics-embedded machine learning performance for streamflow prediction

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年4月2日

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  • Adoubi Vincent De Paul Adombi,
  • Romain Chesnaux

摘要

Physics-embedded machine learning (PeML) models integrate process-based representations with machine learning (ML) components to improve hydrological predictions. Despite their growing adoption, the relative contribution of each component, namely the process-based structure, ML capacity, and coupling interface, remains unclear. To address this, we constructed PeML models by pairing physics-aware recurrent neural networks (PRNNs), derived from four conceptual hydrological models (EXP-HYDRO, HBV, FLEX, and WBM), with a 1D convolutional neural network (1D-CNN) and tested two coupling strategies. Hybrid I inputs both simulated streamflow and meteorological forcings into the 1D-CNN, whereas Hybrid II uses only simulated streamflow. All models were evaluated across 500 basins from the CAMELS-US dataset. Results indicate that PeML models with Hybrid I coupling consistently outperform both standalone PRNNs and the purely data-driven 1D-CNN, with median NSE and KGE above 0.60. Hybrid II models show more variable performance depending on the embedded conceptual model. A systematic sensitivity analysis within the tested architectural configurations shows that the complexity of the 1D-CNN is the dominant factor driving PeML performance, whereas the choice of conceptual model and the input interface have smaller effects. These findings highlight that process-based models provide useful inductive biases, but the design and expressiveness of the ML component primarily determine predictive skill. Although the study offers valuable insights into the relative contribution of each PeML component, its scope, limited to four conceptual models, non-anthropized basins, and a single ML architecture, constrains the generalization of its conclusions. These limitations point toward future investigations that explore alternative PeML designs and more diverse hydrological conditions.