Forecasting GPS displacements with a Long Short-Term Memory (LSTM) network

Precise monitoring of Earth's crustal deformation relies heavily on the analysis of Global Positioning System (GPS) displacement time series recorded by the set of ground-based antennas. This monitoring is possible for the period during which the GPS station is operational. In this presentation, we undertake one of the first attempts to forecast daily GPS displacements for 13 randomly selected stations in Europe, for which the displacements were recorded from 1996 to 2023. We use vertical displacements provided by the Nevada Geodetic Laboratory (NGL) and pre-process them thoroughly. We then apply the Long Short-Term Memory (LSTM) network, one of the Deep Learning approaches, and evaluate its efficiency for long-term forecasting of GPS displacements over two-year horizon. The performance of the data-driven LSTM network is compared against the standard statistical AutoRegressive Integrated Moving Average (ARIMA) prediction method. We also quantify the impact of data pre-processing strategies on forecast accuracy, specifically gap-filling techniques, such as linear interpolation, Piecewise Cubic Hermite Interpolating Polynomial (PCHIP), a seasonality-based Least Squares (LS) reconstruction, and raw data processing without interpolation are assessed. The models were evaluated using Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), and the coefficient of determination (R²). Statistical significance was assessed using the Friedman test followed by the Nemenyi post-hoc test. Results indicate that the LSTM network significantly outperforms the ARIMA model in long-term forecasting. The hybrid approach combining LSTM with LS-based interpolation yielded the highest accuracy. Furthermore, degradation analysis reveals that the LSTM model maintains stability and lower error accumulation over the forecast horizon. These findings indicate that LSTM networks, particularly when combined with seasonality-aware interpolation (LS), offer a significant improvement in forecasting accuracy and stability compared to the standard ARIMA model. The results underscore the substantial potential of deep learning methodologies in geodetic time series analysis, encouraging their further exploration as robust alternatives to statistic approaches.