[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-125181-en":3,"doc-seo-125181-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},125181,1374391975076,"Riley","https://ap-avatar.wpscdn.com/avatar/14000253ca4ec9f6853?x-image-process=image/resize,m_fixed,w_180,h_180&k=1783305029341752051",8,"Research & Report","Short-term prediction of celestial pole offsets with interpretable machine learning","Celestial Pole Offsets (CPO) represent unmodelled signals revealed by the difference between observed and modelled Earth precession/nutation. Although CPO are measured via Very Long Baseline Interferometry (VLBI), the availability of final data series has about four weeks of latency, limiting high-accuracy, real-time Earth-rotation applications such as spacecraft navigation. International IERS rapid CPO products are faster but typically less accurate. This work introduces an operational short-term (30-day) forecasting method based on Neural Additive Models (NAMs), built from long short-term memory networks, with analytical uncertainty quantification and feature-importance interpretability. Using JPL CPO as input, NAMs improve IERS rapid products by 57% for dX and 25% for dY under fully operational conditions, yielding accurate predictions that address latency constraints for real-time use.","Kiani Shahvandi et al.  \nEarth, Planets and Space (2024) 76:18 [https://doi.org/10.1186/s40623-024-01964-2](https://doi.org/10.1186/s40623-024-01964-2)  \nEarth, Planets and Space  \n FULL PAPER Open Access  \nShort-term prediction of celestial pole offsets with interpretable machine learning  \nMostafa Kiani Shahvandi1* , Santiago Belda2, Siddhartha Mishra3 and Benedikt Soja1  \nAbstract  \nThe 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.  \nKeywords Celestial pole offsets, Interpretable machine learning, Neural additive models, Prediction accuracy  \n*Correspondence: Mostafa Kiani Shahvandi[mkiani@ethz.ch](mkiani@ethz.ch)  \nFull list of author information is available at the end of the article  \n© The Author(s) 2024. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit [http://creativecommons.org/licenses/by/4.0/](http://creativecommons.org/licenses/by/4.0/.)[.](http://creativecommons.org/licenses/by/4.0/.)  \nKiani Shahvandi etal. Earth, Planets and Space (2024) 76:18 Page 2 of 15  \nGraphical Abstract  \nIntroduction  \nGravitational effects of the Sun and Moon induce variations in the Earth rotation axis, commonly known as precession and nutation (Gross 2015). In addition, mass redistribution within the Earth system also perturbs the rotation axis of the Earth. The latter can be modulated onto the nutation, generating small oscillatory motions. These motions are irregular and depend on various parameters, including geodynamics of the Earth. Therefore, in contrast to the major components of precession and nutation that are modelled with rigorous theories (e.g. Wahr 1981; Matt","cbCaihIwMXvwYNQS","https://ap.wps.com/l/cbCaihIwMXvwYNQS","pdf",9424403,1,15,"English","en",105,"# Abstract\n# Introduction","[{\"question\":\"What are celestial pole offsets (CPO) and why do they matter?\",\"answer\":\"CPO are unmodelled signals seen in the difference between observed and modelled precession/nutation. They provide two-dimensional information (dX and dY) relevant to Earth rotation and related real-time applications such as navigation.\"},{\"question\":\"Why is predicting CPO challenging in practice?\",\"answer\":\"VLBI observations yield the most accurate final CPO series, but data centers deliver it with nearly four weeks of latency. Rapid products from IERS are available sooner, yet are often less accurate for demanding applications.\"},{\"question\":\"How does the proposed method improve short-term CPO prediction?\",\"answer\":\"The approach uses Neural Additive Models (NAMs) combined with long short-term memory networks to forecast 30-day horizons. It also provides analytical relations for uncertainty quantification and feature importance. Tests using JPL CPO show improved accuracy over IERS rapid products by 57% for dX and 25% for dY under operational conditions.\"}]","Short-term prediction of celestial pole offsets with interpretable machine learning | PDF",1785897243,38,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"short-term-prediction-of-celestial-pole-offsets-with-interpretable-machine-learning","",{"@graph":36,"@context":85},[37,54,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/short-term-prediction-of-celestial-pole-offsets-with-interpretable-machine-learning/125181/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-05",true,{"@type":65,"interactionType":66,"userInteractionCount":4},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What are celestial pole offsets (CPO) and why do they matter?","Question",{"text":75,"@type":76},"CPO are unmodelled signals seen in the difference between observed and modelled precession/nutation. They provide two-dimensional information (dX and dY) relevant to Earth rotation and related real-time applications such as navigation.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"Why is predicting CPO challenging in practice?",{"text":80,"@type":76},"VLBI observations yield the most accurate final CPO series, but data centers deliver it with nearly four weeks of latency. Rapid products from IERS are available sooner, yet are often less accurate for demanding applications.",{"name":82,"@type":73,"acceptedAnswer":83},"How does the proposed method improve short-term CPO prediction?",{"text":84,"@type":76},"The approach uses Neural Additive Models (NAMs) combined with long short-term memory networks to forecast 30-day horizons. It also provides analytical relations for uncertainty quantification and feature importance. 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