Adjoint-based spatially distributed calibration of a grid GR-based parsimonious hydrological model over 312 French catchments with SMASH platform

Colleoni, François; Garambois, Pierre‐André; Javelle, Pierre; Jay-Allemand, Maxime; Arnaud, Patrick

doi:10.5194/egusphere-2022-506

Cited by 2 publications

(1 citation statement)

References 51 publications

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“…Instead of automatically working through the elementary operations as AD does, the adjoint solves another accompanying equation (derived by the modeler based 115 on the chain rule and the associative property of matrix multiplication) to rapidly produce the gradients of outputs with respect to inputs ---more precisely, it computes the vector-Jacobian product. However, the adjoint method has not yet been extensively explored in the context of large-scale, regionalized hydrologic simulations (White et al, 2003;Colleoni et al, 2022), which require mini-batch processing, high data throughput, and a long time for integration. It is unclear if the adjoint method is applicable in this scenario.…”

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confidence: 99%

When ancient numerical demons meet physics-informed machine learning: adjoint-based gradients for implicit differentiable modeling

Song,

Knoben,

Clark

et al. 2023

Preprint

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Abstract. Recent advances in differentiable modeling, a genre of physics-informed machine learning that trains neural networks (NNs) together with process-based equations, has shown promise in enhancing hydrologic models’ accuracy, interpretability, and knowledge-discovery potential. Current differentiable models are efficient for NN-based parameter regionalization, but the simple explicit numerical schemes paired with sequential calculations (operator splitting) can incur large numerical errors whose impacts on models’ representation power and learned parameters are not clear. Implicit schemes, however, cannot rely on automatic differentiation to calculate gradients due to potential issues of gradient vanishing and memory demand. Here we propose a “discretize-then-optimize” adjoint method to enable differentiable implicit numerical schemes for the first time for large-scale hydrologic modeling. The adjoint model demonstrates comprehensively improved performance, with Kling-Gupta efficiency coefficients, peak-flow and low-flow metrics, and evapotranspiration that moderately surpass the already-competitive explicit model. Therefore, the previous sequential-calculation approach had a detrimental impact on the model’s ability to represent hydrologic dynamics. Furthermore, with a structural update that describes capillary rise, the adjoint model can better describe baseflow in arid regions and also produce low and peak flows that outperform even pure machine learning methods such as long short-term memory networks. The adjoint model rectified some parameter distortions but did not alter spatial parameter distributions, demonstrating the robustness of regionalized parameterization. Despite higher computational expenses and modest improvements, the adjoint model’s success removes the barrier for complex implicit schemes to enrich differentiable modeling in hydrology.

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mentioning

confidence: 99%

When ancient numerical demons meet physics-informed machine learning: adjoint-based gradients for implicit differentiable modeling

Song,

Knoben,

Clark

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

When ancient numerical demons meet physics-informed machine learning: adjoint-based gradients for implicit differentiable modeling

Song,

Knoben,

Clark

et al. 2024

Hydrol. Earth Syst. Sci.

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Abstract. Recent advances in differentiable modeling, a genre of physics-informed machine learning that trains neural networks (NNs) together with process-based equations, have shown promise in enhancing hydrological models' accuracy, interpretability, and knowledge-discovery potential. Current differentiable models are efficient for NN-based parameter regionalization, but the simple explicit numerical schemes paired with sequential calculations (operator splitting) can incur numerical errors whose impacts on models' representation power and learned parameters are not clear. Implicit schemes, however, cannot rely on automatic differentiation to calculate gradients due to potential issues of gradient vanishing and memory demand. Here we propose a “discretize-then-optimize” adjoint method to enable differentiable implicit numerical schemes for the first time for large-scale hydrological modeling. The adjoint model demonstrates comprehensively improved performance, with Kling–Gupta efficiency coefficients, peak-flow and low-flow metrics, and evapotranspiration that moderately surpass the already-competitive explicit model. Therefore, the previous sequential-calculation approach had a detrimental impact on the model's ability to represent hydrological dynamics. Furthermore, with a structural update that describes capillary rise, the adjoint model can better describe baseflow in arid regions and also produce low flows that outperform even pure machine learning methods such as long short-term memory networks. The adjoint model rectified some parameter distortions but did not alter spatial parameter distributions, demonstrating the robustness of regionalized parameterization. Despite higher computational expenses and modest improvements, the adjoint model's success removes the barrier for complex implicit schemes to enrich differentiable modeling in hydrology.

show abstract

Adjoint-based spatially distributed calibration of a grid GR-based parsimonious hydrological model over 312 French catchments with SMASH platform

Cited by 2 publications

References 51 publications

When ancient numerical demons meet physics-informed machine learning: adjoint-based gradients for implicit differentiable modeling

When ancient numerical demons meet physics-informed machine learning: adjoint-based gradients for implicit differentiable modeling

When ancient numerical demons meet physics-informed machine learning: adjoint-based gradients for implicit differentiable modeling

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