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This paper proposes a physics-guided machine learning approach that combines machine learning models and physics-based models to improve the prediction of water flow and temperature in river networks. We first build a recurrent graph network model to capture the interactions among multiple segments in the river network. Then we transfer knowledge from physics-based models to guide the learning of the machine learning model. We also propose a new loss function that balances the performance over different river segments. We demonstrate the effectiveness of the proposed method in predicting temperature and streamflow in a subset of the Delaware River Basin. In particular, the proposed method has brought a 33%/14% accuracy improvement over the state-of-the-art physics-based model and 24%/14% over traditional machine learning models (e.g., LSTM) in temperature/streamflow prediction using very sparse (0.1%) training data. The proposed method has also been shown to produce better performance when generalized to different seasons or river segments with different streamflow ranges. 

This paper proposes a physics-guided recurrent neural network model (PGRNN) that combines RNNs and physics-based models to leverage their complementary strengths and improve the modeling of physical processes. Specifically, we show that a PGRNN can improve prediction accuracy over that of physical models, while generating outputs consistent with physical laws, and achieving good generalizability. Standard RNNs, even when producing superior prediction accuracy, often produce physically inconsistent results and lack generalizability. We further enhance this approach by using a pre-training method that leverages the simulated data from a physics-based model to address the scarcity of observed data. Although we present and evaluate this methodology in the context of modeling the dynamics of temperature in lakes, it is applicable more widely to a range of scientific and engineering disciplines where mechanistic (also known as process-based) models are used, e.g., power engineering, climate science, materials science, computational chemistry, and biomedicine. 

Lakes support globally important food webs through algal productivity and contribute significantly to the global carbon cycle. However, predictions of how broad‐scale lake carbon flux and productivity may respond to future climate are extremely limited. Here, we used an integrated modeling framework to project changes in lake‐specific and regional primary productivity and carbon fluxes under 21st century climate for thousands of lakes. We observed high uncertainty in whether lakes collectively were to increase or decrease lake CO₂emissions and carbon burial in our modeled region owing to divergence in projected regional water balance among climate models. Variation in projected air temperature influenced projected changes in lake primary productivity (but not CO₂emissions or carbon burial) as warmer air temperatures decreased productivity through reduced lake water volume. Cross‐scale interactions between regional drivers and local characteristics dictated the magnitude and direction of lake‐specific carbon flux and productivity responses to future climate.