Graph Neural Networks with dilated convolutions for geomagnetic field forecasting: a single-station topological approach
Geomagnetic field forecasting is critical for mitigating space weather hazards, yet single-station prediction remains a challenge due to the complex, non-linear coupling of vector components. In this work, we propose a Graph Neural Network (GNN) architecture enhanced with Temporal Convolutional Networks (TCN) to forecast the H, D, and Z components. By modeling the observatory’s sensors as nodes in a learned directed graph, the system captures dynamic spatio-temporal correlations between orthogonal components. We introduce a dilated inception layer to efficiently capture multi-scale temporal patterns. Experimental results using 1-min downsampled data from the MAGDAS station (Ecuador) show that our model achieves a Mean Absolute Error (MAE) of 0.8036 nT, outperforming Vector Autoregression (VAR) and thoroughly optimized LSTM baselines. While the Naive Persistence baseline yields a marginally lower global MAE due to the statistical dominance of quiet-time periods, the proposed GNN-TCN provides vastly superior phase tracking ( R = 0.9950 ) and structural stability. Rigorous evaluation under varying space weather conditions reveals robust performance, maintaining a highly controlled error even during the top 5% most severe local geomagnetic storms. These findings, supported by power spectral density analysis, indicate that high-frequency fluctuations at a single station are dominated by instrumental and stochastic noise, making temporal filtering via downsampling essential. Ultimately, this proof-of-concept study demonstrates that utilizing a learned adjacency matrix as an adaptable structural regularization, rather than extracting a fixed physical law, provides a highly stable and effective framework for short-term geomagnetic field forecasting.