This paper proposes a new data-driven method for predicting water temperature in stream networks with reservoirs. The water flows released from reservoirs greatly affect the water temperature of downstream river segments. However, the information of released water flow is often not available for many reservoirs, which makes it difficult for data-driven models to capture the impact to downstream river segments. In this paper, we first build a state-aware graph model to represent the interactions amongst streams and reservoirs, and then propose a parallel learning structure to extract the reservoir release information and use it to improve the prediction. In particular, for reservoirs with no available release information, we mimic the water managers' release decision process through a pseudo-prospective learning method, which infers the release information from anticipated water temperature dynamics. For reservoirs with the release information, we leverage a physics-based model to simulate the water release temperature and transfer such information to guide the learning process for other reservoirs. The evaluation for the Delaware River Basin shows that the proposed method brings over 10% accuracy improvement over existing data-driven models for stream temperature prediction when the release data is not available for any reservoirs. The performance is further improved after we incorporate the release data and physical simulations for a subset of reservoirs.

This paper presents a physics-guided machine learning approach that incorporates partial differential equations (PDEs) in a graph neural network model to improve the prediction of water temperature in river networks. The standard graph neural network model often uses pre-defined edge weights based on distance or similarity measures. Such static graph structure can be limited in capturing multiple processes in a physical system that interact and evolve over time. The limitation to represent underlying physical processes can severely affect the performance of the predictive model, especially when we have access to limited training data. To better capture the dynamic interactions among multiple segments in a river network, we built a dynamic graph model, where the graph structure is driven by the PDE that describes underlying physical processes. We further combine the dynamic graph structure and the recurrent layers to model temporal dependencies and improve the prediction. We demonstrate the effectiveness of the proposed method in a subnetwork of the Delaware River Basin. In particular, we show that the proposed method outperforms existing physics-based and machine learning models in temperature prediction using sparse observation data for training. The proposed method has also been shown to produce better performance when generalized to different seasons.

Accurate prediction of water temperature in streams is critical for monitoring and understanding biogeochemical and ecological processes in streams. Stream temperature is affected by weather patterns (such as solar radiation) and water flowing through the stream network. Additionally, stream temperature can be substantially affected by water releases from man-made reservoirs to downstream segments. In this paper, we propose a heterogeneous recurrent graph model to represent these interacting processes that underlie stream-reservoir networks and improve the prediction of water temperature in all river segments within a network. Because reservoir release data may be unavailable for certain reservoirs, we further develop a data assimilation mechanism to adjust the deep learning model states to correct for the prediction bias caused by reservoir releases. Our evaluation for the Delaware River Basin has demonstrated the superiority of our proposed method over multiple existing methods. We have extensively studied the effect of the data assimilation mechanism under different scenarios.

This paper proposes a new physics-guided machine learning approach that incorporates the scientific knowledge in physics-based models into machine learning models. Physics-based models are widely used to study dynamical systems in a variety of scientific and engineering problems. Although they are built based on general physical laws that govern the relations from input to output variables, these models often produce biased simulations due to inaccurate parameterizations or approximations used to represent the true physics. In this paper, we aim to build a new data-driven framework to monitor dynamical systems by extracting general scientific knowledge embodied in simulation data generated by the physics-based model. To handle the bias in simulation data caused by imperfect parameterization, we propose to extract general physical relations jointly from multiple sets of simulations generated by a physics-based model under different physical parameters. In particular, we develop a spatio-temporal network architecture that uses its gating variables to capture the variation of physical parameters. We initialize this model using a pre-training strategy that helps discover common physical patterns shared by different sets of simulation data. Then we fine-tune it using limited observation data via a contrastive learning process. By leveraging the complementary strength of machine learning and domain knowledge, our method has been shown to produce accurate predictions, use less training samples and generalize to out-of-sample scenarios. We further show that the method can provide insights about the variation of physical parameters over space and time in two domain applications: predicting temperature in streams and predicting temperature in lakes.

Effective training of advanced ML models requires large amounts of labeled data, which is often scarce in scientific problems given the substantial human labor and material cost to collect labeled data. This poses a challenge on determining when and where we should deploy measuring instruments (e.g., in-situ sensors) to collect labeled data efficiently. This problem differs from traditional pool-based active learning settings in that the labeling decisions have to be made immediately after we observe the input data that come in a time series. In this paper, we develop a real-time active learning method that uses the spatial and temporal contextual information to select representative query samples in a reinforcement learning framework. To reduce the need for large training data, we further propose to transfer the policy learned from simulation data which is generated by existing physics-based models. We demonstrate the effectiveness of the proposed method by predicting streamflow and water temperature in the Delaware River Basin given a limited budget for collecting labeled data. We further study the spatial and temporal distribution of selected samples to verify the ability of this method in selecting informative samples over space and time.

This paper proposes a physics-guided machine learning approach that combines machine learning models and physicsbased 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.