High-Precision Ground Characterization of Test-Mass Magnetic Properties for the Taiji Gravitational Wave Mission via a Physics-Informed Neural Framework

Abstract

Taiji is a gravitational wave detection mission in space initiated by the Chinese Academy of Sciences, which will open the millihertz window through a heliocentric triangular constellation of three drag-free spacecraft. Its ultimate sensitivity is determined partly by the residual acceleration noise of the gravitational reference sensors (GRS), within which the coupling between the test-mass and the fluctuating environmental magnetic field constitutes one of the key stray-force contributions. Following the path established by the LISA and TianQin teams, high-precision ground characterization of remanent magnetic moment $\vec{m}_r$ and volume susceptibility $\chi$ of the test masses is a central step in the Taiji pre-launch test program. A persistent challenge for this characterization is the non-stationary, colored background noise inherent to torsion-pendulum facilities, which systematically biases classical Ordinary Least Squares (OLS) and Kalman filter (KF) estimators. We propose an AI-enhanced Differentiable Weighted Least Squares (AI-WLS) framework that fuses a dilated one-dimensional residual network, acting as a dynamic noise evaluator, with a fully differentiable analytical physical solver. This architecture preserves the exact linear mapping from the magnetic parameters to the torque response while autonomously identifying and suppressing contaminated data segments. Validated on real measured noise from the Changchun Institute of Optics, Fine Mechanics and Physics torsion-pendulum facility developed for Taiji, which achieves a torque sensitivity of order $10^{-13}\,\mathrm{N\cdot m\,Hz^{-1/2}}$, the AI-WLS framework bounds the maximum absolute estimation errors at $4.46\times 10^{-10}\,\mathrm{A\cdot m^2}$ for $\vec{m}_r$ and $7.8\times 10^{-8}$ for $\chi$, satisfying Taiji's ground-test requirements on all these parameters simultaneously.