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Abstract. As a genre of physics-informed machine learning, differentiable process-based hydrologic models (abbreviated as δ or delta models) with regionalized deep-network-based parameterization pipelines were recently shown to provide daily streamflow prediction performance closely approaching that of state-of-the-art long short-term memory (LSTM) deep networks. Meanwhile, δ models provide a full suite of diagnostic physical variables and guaranteed mass conservation. Here, we ran experiments to test (1) their ability to extrapolate to regions far from streamflow gauges and (2) their ability to make credible predictions of long-term (decadal-scale) change trends. We evaluated the models based on daily hydrograph metrics (Nash–Sutcliffe model efficiency coefficient, etc.) and predicted decadal streamflow trends. For prediction in ungauged basins (PUB; randomly sampled ungauged basins representing spatial interpolation), δ models either approached or surpassed the performance of LSTM in daily hydrograph metrics, depending on the meteorological forcing data used. They presented a comparable trend performance to LSTM for annual mean flow and high flow but worse trends for low flow. For prediction in ungauged regions (PUR; regional holdout test representing spatial extrapolation in a highly data-sparse scenario), δ models surpassed LSTM in daily hydrograph metrics, and their advantages in mean and high flow trends became prominent. In addition, an untrained variable, evapotranspiration, retained good seasonality even for extrapolated cases. The δ models' deep-network-based parameterization pipeline produced parameter fields that maintain remarkably stable spatial patterns even in highly data-scarce scenarios, which explains their robustness. Combined with their interpretability and ability to assimilate multi-source observations, the δ models are strong candidates for regional and global-scale hydrologic simulations and climate change impact assessment.
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This content will become publicly available on January 1, 2026
A Fluid Flow‐Based Deep Learning (FFDL) Architecture for Subsurface Flow Systems With Application to Geologic CO 2 Storage
Abstract Prediction of the spatial‐temporal dynamics of the fluid flow in complex subsurface systems, such as geologic storage, is typically performed using advanced numerical simulation methods that solve the underlying governing physical equations. However, numerical simulation is computationally demanding and can limit the implementation of standard field management workflows, such as model calibration and optimization. Standard deep learning models, such as RUNET, have recently been proposed to alleviate the computational burden of physics‐based simulation models. Despite their powerful learning capabilities and computational appeal, deep learning models have important limitations, including lack of interpretability, extensive data needs, weak extrapolation capacity, and physical inconsistency that can affect their adoption in practical applications. We develop a Fluid Flow‐based Deep Learning (FFDL) architecture for spatial‐temporal prediction of important state variables in subsurface flow systems. The new architecture consists of a physics‐based encoder to construct physically meaningful latent variables, and a residual‐based processor to predict the evolution of the state variables. It uses physical operators that serve as nonlinear activation functions and imposes the general structure of the fluid flow equations to facilitate its training with data pertaining to the specific subsurface flow application of interest. A comprehensive investigation of FFDL, based on a field‐scale geologic storage model, is used to demonstrate the superior performance of FFDL compared to RUNET as a standard deep learning model. The results show that FFDL outperforms RUNET in terms of prediction accuracy, extrapolation power, and training data needs.
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- Award ID(s):
- 2425919
- PAR ID:
- 10632328
- Publisher / Repository:
- Water Resources Research
- Date Published:
- Journal Name:
- Water Resources Research
- Volume:
- 61
- Issue:
- 1
- ISSN:
- 0043-1397
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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