Feature Selection and Deep Learning for Simultaneous Forecasting of Celestial Pole Offset (CPO) and Polar Motion (PM)

Accurate prediction of Earth orientation parameters (EOPs) is critical for astro-geodynamics, high-precision space navigation, and positioning, and deep space exploration. However, the current models' prediction accuracy for EOPs is significantly lower than that of geodetic technical solutions, which can adversely affect certain high-precision real-time users. In this study, we introduce a simultaneous prediction approach for Polar Motion (PM) and Celestial Pole Offsets (CPO) employing deep neural networks, aiming to deliver precise predictions for both parameters.
The methodology comprises three components, with the first being feature interaction and selection. The process of feature selection within the context of deep learning differs from traditional methods for machine learning, and may not be directly applicable to theme since they are designed to automatically learn relevant features. Consequently, we propose in this step a solution based on feature engineering to select the best set of variables that can keep the model as simple as possible but with enough precision and accuracy using recursive feature elimination and the SHAP value algorithm, aiming to investigate the influence of FCN (Free Core Nutation) with its amplitude and phase on the CPO forecasting. This investigation is crucial since FCN is the main source of variance of the CPO series. Considering the role represented by the effective Angular Momentum functions (EAM), and their direct influence on the Earth's rotation, it is logical to assess numerically the impact of EAM on the Polar motion and FCN excitations. SHAP value aids in comprehending how each feature contributes to final predictions, highlighting the significance of each feature relative to others,  and revealing the model's dependency on feature interactions.
During the second phase, we formulate two deep-learning methods for each parameter. The first Neural Network incorporates all features, while the second focuses on the subset of features identified in the initial step. This stage primarily involves exploring feature and hyperparameter tuning to enhance model performance. The SHAP value algorithm is also used in this stage for interpretation. 
In the final phase, we construct a multi-task deep learning model designed to simultaneously predict ( CPO ) and ( PM ).  This model is built using the optimal set of features and hyperparameters identified in the preceding steps. To validate the methodology, we employ the most recent version of the time series from the International Earth Rotation and Reference Systems Service (IERS), namely IERS 20 C04 and EAM provided by the German Research Center for Geosciences (GFZ). We focus on a forecasting horizon of 90 days, the practical forecasting horizon needed in space-geodetic applications.
In the end, we conclude that the developed model is proficient in simultaneously predicting ( CPO ) and ( PM ). The incorporation of ( EAM ), sheds light on its role in CPO excitations and Polar Motion predictions.