A Graph Attention Framework with Kinematic Constraints for Network-Based GNSS Time Series Prediction

Abstract Predicting GNSS displacement time series accurately is challenging due to complex spatial dependencies, multi-source noise, and hyperparameter tuning difficulties. Based on this, We propose a Bayesian-optimized DA-GAT-BiLSTM model with a kinematically-motivated Direction Loss. The framework combines a KNN-based geodesic station graph with graph attention for spatial encoding, BiLSTM for temporal modelling, and a direction-aware head for coupled E/N/U prediction. A kinematically-motivated Direction Loss enforces smoothness and cross-component consistency, with Optuna-based optimization for efficient hyperparameter selection, aiming to enable a novel network-based prediction through inter-station information sharing. Using data from 100 stations worldwide (2000–2024), spatial autocorrelation (Moran’s I = 0.550/0.625/0.585 for E/N/U) supports a sparse kNN geodesic prior (k = 10), enabling DA-GAT-BiLSTM to deliver millimetre-level E/N/U prediction (R² = 0.948/0.964/0.937; mean residuals − 0.11/-0.04/0.14 mm for E/N/U). Ablations confirm that graph attention is critical (MAE + 72–76%; R² −9–14% without GAT), the direction-aware head improves robustness—especially vertically (MAE + 40–45% without DA)—and the kinematically-motivated Direction Loss outperforms MSE on high-quality stations (MAE − 23–37%, RMSE − 24–38%, R² +0.09–0.14). Optuna achieves a lower validation loss (0.104 in 12.5 h) than grid (0.145 in 48.5 h) or random search (0.118) Comparison with VARIMA, GCN-LSTM, and GAT-Transformer shows that DA-GAT-BiLSTM achieves lower prediction errors across displacement components, with performance differences corresponding to the presence of adaptive spatial attention, bidirectional temporal encoding, and direction-aware cross-component modelling. The proposed framework offers a reliable tool for crustal deformation monitoring and early-warning applications.