Uncertainty-Aware Graph Neural Reconstruction of Urban Temperature Fields from Sparse Sensors under Deployment Constraints
2026-06-01 • Machine Learning
Machine Learning
AI summaryⓘ
The authors developed a method using graph neural networks (GNNs) to estimate daily maximum temperatures across a city area from a limited number of sensors. Their approach also predicts how confident the model is about these temperature estimates. They tested different ways to decide where to place sensors, ensuring they are at least 4 km apart, and found their method predicts temperatures more accurately than traditional spatial methods like kriging. The study shows that having about 30 well-placed sensors balances accuracy and spacing constraints well. This method can help cities monitor heat risks with fewer sensors while understanding uncertainty.
graph neural networktemperature reconstructionsensor placementpredictive uncertaintygraph attentionmean-residual architectureGaussian negative log-likelihoodProper Orthogonal DecompositionQR factorizationkriging
Authors
Reda Snaiki, Abdelatif Merabtine
Abstract
Reconstructing spatially continuous daily temperature fields from sparse observations is important for urban climate monitoring and heat-risk analysis, but practical deployments are limited by sensor budgets and spacing constraints. This study proposes an uncertainty-aware graph neural network (GNN) framework for reconstructing daily maximum temperature fields from sparse sensors while supporting distance-constrained sensor placement and probabilistic exceedance mapping. The model predicts both the temperature field and a spatially varying predictive uncertainty field using a graph-attention-based mean-residual architecture trained with a Gaussian negative log-likelihood. Sensor placement is addressed using a Proper Orthogonal Decomposition with QR factorization (POD-QR) strategy with a 4 km minimum inter-sensor distance constraint and is compared with random feasible placement and farthest-point sampling. The framework is evaluated over a Montreal-area polygon using Daymet v4.1 daily temperature data (1 km resolution) under a strict temporal hold-out protocol (training: 2020-2023; testing: 2024). Across sensor budgets (10-40 sensors), the proposed GNN consistently outperforms inverse distance weighting and ordinary kriging in RMSE and MAE on unobserved nodes. Sensor-placement effects are most pronounced at low budgets and diminish at higher budgets, with a practical saturation regime emerging around 30 sensors under the imposed spacing constraint. Probabilistic evaluation further shows improved uncertainty calibration with increasing sensor density and a better sharpness-calibration trade-off than kriging. These results support the proposed framework as an effective tool for uncertainty-aware temperature field reconstruction and decision-oriented heat-risk mapping.