Recurrent neural network trained with the extended Kalman filter to forecast the geomagnetic secular variation for IGRF-14

Recurrent neural network trained with the extended Kalman filter to forecast the geomagnetic secular variation for IGRF-14 | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Recurrent neural network trained with the extended Kalman filter to forecast the geomagnetic secular variation for IGRF-14 Sho Sato, Shin’ya Nakano, Vincent Lesur, Masaki Matsushima, Takuto Minami, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7405758/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 27 Jan, 2026 Read the published version in Earth, Planets and Space → Version 1 posted 5 You are reading this latest preprint version Abstract This study proposes a neural network approach for predicting the geomagnetic secular variation (SV) to improve the accuracy and efficiency of short-term geomagnetic forecasts. The International Geomagnetic Reference Field (IGRF), updated every five years, provides a standardized representation of Earth’s magnetic field, including a five-year linear prediction of SV. Recent forecasting methods, which are reliant on computationally intensive geodynamo simulations, often struggle to capture sudden changes due to nonlinearity, such as the geomagnetic jerk. We have developed a novel recurrent neural network (RNN) framework trained using the extended Kalman filter (EKF), termed the EKF-RNN, to address these challenges. Unlike conventional backpropagation methods, the EKF dynamically updates the RNN weights by incorporating error covariance from training data, effectively mitigating overfitting while preserving computational efficiency. The EKF-RNN model is validated through hindcast experiments for epochs 2004.87 to 2014.62, utilizing geomagnetic field snapshots derived from magnetic observatory hourly means and CHAMP and Swarm-A satellite data. The results exhibit forecast errors below 85 nT for five-year predictions, outperforming known data assimilation methods such as 4dEnVar. Additionally, the EKF-RNN method provides forecast error covariance matrices, offering enhanced interpretability and robustness compared to earlier neural network models. This research underscores the potential of EKF-RNN for reliable geomagnetic SV predictions, contributing to the accuracy of the 14th-generation IGRF and advancing data-driven approaches in geomagnetic field modeling. Geomagnetic Secular Variation International Geomagnetic Reference Field (IGRF) Machine Learning Extended Kalman Filter Recurrent Neural Network Full Text Supplementary Files GraphicalAbstract.png Cite Share Download PDF Status: Published Journal Publication published 27 Jan, 2026 Read the published version in Earth, Planets and Space → Version 1 posted Reviewers agreed at journal 15 Sep, 2025 Reviewers invited by journal 15 Sep, 2025 Editor assigned by journal 09 Sep, 2025 First submitted to journal 07 Sep, 2025 Editorial decision: Minor Revision 26 Aug, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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The International Geomagnetic Reference Field (IGRF), updated every five years, provides a standardized representation of Earth’s magnetic field, including a five-year linear prediction of SV. Recent forecasting methods, which are reliant on computationally intensive geodynamo simulations, often struggle to capture sudden changes due to nonlinearity, such as the geomagnetic jerk. We have developed a novel recurrent neural network (RNN) framework trained using the extended Kalman filter (EKF), termed the EKF-RNN, to address these challenges. Unlike conventional backpropagation methods, the EKF dynamically updates the RNN weights by incorporating error covariance from training data, effectively mitigating overfitting while preserving computational efficiency. The EKF-RNN model is validated through hindcast experiments for epochs 2004.87 to 2014.62, utilizing geomagnetic field snapshots derived from magnetic observatory hourly means and CHAMP and Swarm-A satellite data. 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