Stochastic Spin Modeling and ANEU-TCN for Directional Magnetic Noise Estimation in Atomic Comagnetometers

Atomic comagnetometers based on hybrid spin ensembles are widely used in precision tests of fundamental physics and ultra-sensitive inertial sensing, but their performance can be limited by transverse magnetic noise whose impact depends on both power and direction. This work develops a unified framework for directional transverse-noise analysis and inference by combining a stochastic spin-noise model with an uncertainty-aware temporal convolutional network. The coupled alkali–noble-gas spin dynamics are formulated as a four-dimensional linear stochastic differential equation driven by directional transverse magnetic noise, from which angle-resolved covariance and power spectral density expressions are derived. These results reveal operating-point-dependent anisotropic spin-noise statistics and show that the hybrid spin resonance (HSR) vicinity provides particularly strong directional discriminability. To infer the noise direction from two-channel spin-noise time series, an Angle-aware Noise Estimation with Uncertainty based on temporal convolutional network (ANEU-TCN) is developed using double-angle circular regression and Monte Carlo Dropout. Validation on an experimentally acquired HSR dataset yields a mean absolute error of 0 . 524 ∘ and a root mean square error of 0 . 670 ∘ , while the predicted uncertainty intervals remain conservative on the validation set. These results support accurate, uncertainty-aware directional-noise estimation and noise-aware self-calibration of atomic comagnetometers in complex magnetic environments.