This work introduces a novel graph neural networks (GNNs)-based method to predict stream water temperature and reduce model bias across locations of different income and education levels. Traditional physics-based models often have limited accuracy because they are necessarily approximations of reality. Recently, there has been an increasing interest of using GNNs in modeling complex water dynamics in stream networks. Despite their promise in improving the accuracy, GNNs can bring additional model bias through the aggregation process, where node features are updated by aggregating neighboring nodes. The bias can be especially pronounced when nodes with similar sensitive attributes are frequently connected. We introduce a new method that leverages physical knowledge to represent the node influence in GNNs, and then utilizes physics-based influence to refine the selection and weights over the neighbors. The objective is to facilitate equitable treatment over different sensitive groups in the graph aggregation, which helps reduce spatial bias over locations, especially for those in underprivileged groups. The results on the Delaware River Basin demonstrate the effectiveness of the proposed method in preserving equitable performance across locations in different sensitive groups.

Accurate prediction of water quality and quantity is crucial for sustainable development and human well-being. However, existing data-driven methods often suffer from spatial biases in model performance due to heterogeneous data, limited observations, and noisy sensor data. To overcome these challenges, we propose Fair-Graph, a novel graph-based recurrent neural network that leverages interrelated knowledge from multiple rivers to predict water flow and temperature within large-scale stream networks. Additionally, we introduce node-specific graph masks for information aggregation and adaptation to enhance prediction over heterogeneous river segments. To reduce performance disparities across river segments, we introduce a centralized coordination strategy that adjusts training priorities for segments. We evaluate the prediction of water temperature within the Delaware River Basin, and the prediction of streamflow using simulated data from U.S. National Water Model in the Houston River network. The results showcase improvements in predictive performance and highlight the proposed model's ability to maintain spatial fairness over different river segments.

This paper proposes a graph-based meta learning approach to separately predict water quantity and quality variables for river segments in stream networks. Given the heterogeneous water dynamic patterns in large-scale basins, we introduce an additional meta-learning condition based on physical characteristics of stream segments, which allows learning different sets of initial parameters for different stream segments. Specifically, we develop a representation learning method that leverages physical simulations to embed the physical characteristics of each segment. The obtained embeddings are then used to cluster river segments and add the condition for the meta-learning process. We have tested the performance of the proposed method for predicting daily water temperature and streamflow for the Delaware River Basin (DRB) over a 14 year period. The results confirm the effectiveness of our method in predicting target variables even using sparse training samples. We also show that our method can achieve robust performance with different numbers of clusterings.

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.

In this paper, we introduce a new paradigm that combines scientific knowledge within process-based models and machine learning models to advance scientific discovery in many physical systems. We will describe how to incorporate physical knowledge in real-world dynamical systems as additional constraints for training machine learning models and how to leverage the hidden knowledge encoded by existing process-based models. We evaluate this approach on modeling lake water temperature and demonstrate its superior performance using limited training data and the improved generalizability to different scenarios.

We propose a nonlinear manifold learning technique based on deep convolutional autoencoders that is appropriate for model order reduction of physical systems in complex geometries. Convolutional neural networks have proven to be highly advantageous for compressing data arising from systems demonstrating a slow-decaying Kolmogorov $n$-width. However, these networks are restricted to data on structured meshes. Unstructured meshes are often required for performing analyses of real systems with complex geometry. Our custom graph convolution operators based on the available differential operators for a given spatial discretization effectively extend the application space of deep convolutional autoencoders to systems with arbitrarily complex geometry that are typically discretized using unstructured meshes. We propose sets of convolution operators based on the spatial derivative operators for the underlying spatial discretization, making the method particularly well suited to data arising from the solution of partial differential equations. We demonstrate the method using examples from heat transfer and fluid mechanics and show better than an order of magnitude improvement in accuracy over linear methods.