Deep ensemble geophysics-informed neural networks for the prediction of celestial pole offsets

Celestial Pole Offsets (CPO), denoted by dX and dY, describe the differences in the observed position of the pole in the celestial frame with respect to a certain precession-nutation model. Precession and nutation components are part of the transformation matrix between terrestrial and celestial systems. Therefore, various applications in geodetic science such as high-precision spacecraft navigation require information regrading precession and nutation. For this purpose, CPO can be added to the precession-nutation model to precisely describe the motion of the celestial pole. However, as Very Long Baseline Interferometry (VLBI)-currently the only technique providing CPO-requires long data processing times resulting in several weeks of latency, predictions of CPO become necessary. Here we present a new methodology named Deep Ensemble Geophysics-Informed Neural Networks (DEGINNs) to provide accurate CPO predictions. The methodology has three main elements: (1) deep ensemble learning to provide the prediction uncertainty; (2) broad-band Liouville equation as a geophysical constraint connecting the rotational dynamics of CPO to the atmospheric and oceanic Effective Angular Momentum (EAM) functions and (3) coupled oscillatory recurrent neural networks to model the sequential characteristics of CPO time-series, also capable of handling irregularly sampled time-series. To test the methodology, we use the newest version of the final CPO time-series of International Earth Rotation and Reference Systems Service (IERS), namely IERS 20 C04. We focus on a forecasting horizon of 90 days, the practical forecasting horizon needed in space-geodetic applications. Furthermore, for validation purposes we generate an independent global VLBI solution for CPO since 1984 up to the end of 2022 and analyse the series. We draw the following conclusions. First, the prediction performance of DEGINNs demonstrates up to 25 and 33 percent improvement, respectively, for dX and dY, with respect to the rapid data provided by IERS. Secondly, predictions made with the help of EAM are more accurate compared to those without EAM, thus providing a clue to the role of atmosphere and ocean on the excitation of CPO. Finally, free core nutation period shows temporal variations with a dominant periodicity of around one year, partially excited by EAM.