A precise magnetic modeling method for scientific satellites based on a self-attention mechanism and Kolmogorov-Arnold networks

As the complexity of scientific satellite missions increases, the requirements for their magnetic fields, magnetic field fluctuations, and even magnetic field gradients and variations become increasingly stringent. Additionally, there is a growing need to address the alternating magnetic fields produced by the spacecraft itself. This paper introduces a novel modeling method for spacecraft magnetic dipoles using an integrated self-attention mechanism and a transformer combined with Kolmogorov-Arnold Networks. The self-attention mechanism captures correlations among globally sparse data, establishing dependencies between sparse magnetometer readings. Concurrently, the Kolmogorov-Arnold network, proficient in modeling implicit numerical relationships between data features, enhances the ability to learn subtle patterns. Comparative experiments validate the capability of the proposed method to precisely model magnetic dipoles, achieving maximum Root Mean Square Errors of 24.06 mA·m² and 0.32 cm for size and location modeling, respectively. The spacecraft magnetic model established using this method accurately computes magnetic fields and alternating magnetic fields at designated surfaces or points. This approach facilitates the rapid and precise construction of individual and complete spacecraft magnetic models, enabling the verification of magnetic specifications from the spacecraft design phase.