Physics-Guided Fair Graph Sampling for Water Temperature Prediction in River Networks

TL;DR

This work tackles spatial fairness in river network temperature prediction by blending physics with graph neural networks. The proposed PGFG framework computes physics-based node influence and uses an edge modifier to balance aggregation across sensitive groups, addressing biases arising from network structure and advection dynamics. The approach demonstrates improved fairness (lower disparities and worse-case errors) without sacrificing predictive accuracy on the Delaware River Basin dataset, using PDE-informed relationships and physics-based simulations to guide edge modifications. The methodology generalizes to other environmental modeling tasks, offering a principled way to integrate physical knowledge with fairness-aware graph learning.

Abstract

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.

Figures (6)

• Figure 1: The distribution of RMSE for a GNN model's predictions in different sensitive values, (a) annual household income in USD, (b) education level as the proportion of the population that has attended college relative to the total population, in our study region in the Delaware River Basin.
• Figure 2: (a) A diagram of the proposed model. For each node $i$ and each time $t$, the long short-term memory (LSTM) network extracts an embedding $\textbf{h}_{i,t}$. Then we apply a graph neural network (GNN) to refine each time's embedding by aggregating information from neighboring nodes (highlighted in blue and green), producing a new embedding $\textbf{z}_{i,t}$. Finally, the fully connected layers output the prediction $\hat{\textbf{y}}_i^t$. (b) Fair edge sampling for discrete and continuous sensitive attributes.
• Figure 3: Group fairness comparison amongst PGFG, SLDSGNN, FairGNN, and GraphSAGE over the two different sensitive attributes. The lower value indicates less bias.
• Figure 4: Continuous fairness comparison amongst PGFG, SLDSGNN, FairGNN, and GraphSAGE over the two different sensitive attributes. The lower value indicates less bias.
• Figure 5: The distributions of predictive root mean squared error (RMSE) by (a) GraphSAGE, (b) FairGNN, and (c) the proposed physics-guided fair graph (PGFG) model in three groups. The first row shows the performance in low-income communities, the second row shows the performance in middle-income communities, and the third row shows the performance in high-income communities. The red color indicates worse RMSE.