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Magnetic Field Data Calibration with Transformer Model Using Physical Constraints: A Scalable Method for Satellite Missions, Illustrated by Tianwen-1

Beibei Li, Yutian Chi, Yuming Wang

TL;DR

The paper tackles noisy magnetometer data from space missions, exemplified by Tianwen-1, and proposes a physics‑informed Transformer calibration framework that embeds Maxwell's equations into the learning process. It introduces two Transformer architectures— a standard Transformer and a Physics Informed Transformer with a Fourier Transform branch and a divergence-free constraint—to achieve fast, physically consistent data correction. The approach reduces calibration time from days to minutes or hours and achieves mean absolute errors around $0.513\,\mathrm{nT}$ (Transformer) and $0.44\,\mathrm{nT}$ (Physics Informed Transformer), demonstrating strong agreement with physical models. This method offers scalable, near real-time data calibration for space weather modeling and can be extended to future missions like Tianwen-2, enabling more reliable analyses of planetary magnetospheres and solar wind interactions.

Abstract

This study introduces a novel approach that integrates the magnetic field data correction from the Tianwen-1 Mars mission with a neural network architecture constrained by physical principles derived from Maxwell's equation equations. By employing a Transformer based model capable of efficiently handling sequential data, the method corrects measurement anomalies caused by satellite dynamics, instrument interference, and environmental noise. As a result, it significantly improves both the accuracy and the physical consistency of the calibrated data. Compared to traditional methods that require long data segments and manual intervention often taking weeks or even months to complete this new approach can finish calibration in just minutes to hours, and predictions are made within seconds. This innovation not only accelerates the process of space weather modeling and planetary magnetospheric studies but also provides a robust framework for future planetary exploration and solar wind interaction research.

Magnetic Field Data Calibration with Transformer Model Using Physical Constraints: A Scalable Method for Satellite Missions, Illustrated by Tianwen-1

TL;DR

The paper tackles noisy magnetometer data from space missions, exemplified by Tianwen-1, and proposes a physics‑informed Transformer calibration framework that embeds Maxwell's equations into the learning process. It introduces two Transformer architectures— a standard Transformer and a Physics Informed Transformer with a Fourier Transform branch and a divergence-free constraint—to achieve fast, physically consistent data correction. The approach reduces calibration time from days to minutes or hours and achieves mean absolute errors around (Transformer) and (Physics Informed Transformer), demonstrating strong agreement with physical models. This method offers scalable, near real-time data calibration for space weather modeling and can be extended to future missions like Tianwen-2, enabling more reliable analyses of planetary magnetospheres and solar wind interactions.

Abstract

This study introduces a novel approach that integrates the magnetic field data correction from the Tianwen-1 Mars mission with a neural network architecture constrained by physical principles derived from Maxwell's equation equations. By employing a Transformer based model capable of efficiently handling sequential data, the method corrects measurement anomalies caused by satellite dynamics, instrument interference, and environmental noise. As a result, it significantly improves both the accuracy and the physical consistency of the calibrated data. Compared to traditional methods that require long data segments and manual intervention often taking weeks or even months to complete this new approach can finish calibration in just minutes to hours, and predictions are made within seconds. This innovation not only accelerates the process of space weather modeling and planetary magnetospheric studies but also provides a robust framework for future planetary exploration and solar wind interaction research.
Paper Structure (15 sections, 8 figures)

This paper contains 15 sections, 8 figures.

Table of Contents

  1. Introduction
  2. Methods
  3. Traditional Magnetometer Calibration Methods
  4. Machine Learning Methods
  5. Data
  6. Input
  7. Output
  8. Neural Network Architecture
  9. Transformer
  10. Physics Informed Transformer with Fourier Transform and Physics Constraint
  11. Fourier Transform Layer Structure
  12. Physics Informed Structure
  13. Results
  14. Discussion
  15. Conclusion

Figures (8)

  • Figure 1: Physics Informed Transformer with Fourier Transform and Physics Constraint
  • Figure 2: Comparison of Predicted Results and Actual Data on 2021-11-20
  • Figure 3: Comparison of Predicted Results and Actual Data on 2021-11-21
  • Figure 4: Comparison of Predicted Results and Actual Data on 2021-11-22
  • Figure 5: Comparison of Predicted Results and Actual Data on 2021-11-23
  • ...and 3 more figures