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The difference between observed and modelled precession/nutation reveals unmodelled signals commonly referred to as Celestial Pole Offsets (CPO), denoted by dX and dY. CPO are currently observed only by Very Long Baseline Interferometry (VLBI), but there is nearly 4 weeks of latency by which the data centers provide the most accurate, final CPO series. This latency problem necessitates predicting CPO for high-accuracy, real-time applications that require information regarding Earth rotation, such as spacecraft navigation. Even though the International Earth Rotation and Reference Systems Service (IERS) provides so-called rapid CPO, they are usually less accurate and therefore, may not satisfy the requirements of the mentioned applications. To enhance the quality of CPO predictions, we present a new methodology based on Neural Additive Models (NAMs), a class of interpretable machine learning algorithms. We formulate the problem based on long short-term memory neural networks and derive simple analytical relations for the quantification of prediction uncertainty and feature importance, thereby enhancing the intelligibility of predictions made by machine learning. We then focus on the short-term prediction of CPO with a forecasting horizon of 30 days. We develop an operational framework that consistently provides CPO predictions. Using the CPO series of Jet Propulsion Laboratory as the input to the algorithm, we show that NAMs predictions improve the IERS rapid products on average by 57% for dX and 25% for dY under fully operational conditions. Our predictions are both accurate and overcome the latency issue of final CPO series and thus, can be used in real-time applications. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We present a novel active learning algorithm, termed as iterative surrogate model optimization (ISMO), for robust and efficient numerical approximation of PDE constrained optimization problems. This algorithm is based on deep neural networks and its key feature is the iterative selection of training data through a feedback loop between deep neural networks and any underlying standard optimization algorithm. Numerical examples for optimal control, parameter identification and shape optimization problems for PDEs are provided to demonstrate that ISMO significantly outperforms a standard deep neural network based surrogate optimization algorithm as well as standard optimization algorithms. [ABSTRACT FROM AUTHOR]