Probing Three-Dimensional Magnetic Fields: II -- An Interpretable Convolutional Neural Network

Abstract

Observing 3D magnetic fields, including orientation and strength, within the interstellar medium is vital but notoriously difficult. However, recent advances in our understanding of anisotropic magnetohydrodynamic (MHD) turbulence demonstrate that MHD turbulence and 3D magnetic fields leave their imprints on the intensity features of spectroscopic observations. Leveraging these theoretical frameworks, we propose a novel Convolutional Neural Network (CNN) model to extract this embedded information, enabling the probe of 3D magnetic fields. This model examines not only the plane-of-the-sky magnetic field orientation ($ϕ$), but also the magnetic field's inclination angle ($γ$) relative to the line-of-sight, and the total magnetization level (M$_A^{-1}$) of the cloud. We train the model using synthetic emission lines of $^{13}$CO (J = 1 - 0) and C$^{18}$O (J = 1 - 0), generated from 3D MHD simulations that span conditions from sub-Alfvénic to super-Alfvénic molecular clouds. Our tests confirm that the CNN model effectively reconstructs the 3D magnetic field topology and magnetization. The median uncertainties are under $5^\circ$ for both $ϕ$ and $γ$, and less than 0.2 for M$_A$ in sub-Alfvénic conditions (M$_A\approx0.5$). In super-Alfvénic scenarios (M$_A\approx2.0$), they are under $15^\circ$ for $ϕ$ and $γ$, and 1.5 for M$_A$. We applied this trained CNN model to the L1478 molecular cloud. Results show a strong agreement between the CNN-predicted magnetic field orientation and that derived from Planck 353 GHz polarization data. The CNN approach enabled us to construct the 3D magnetic field map for L1478, revealing a global inclination angle of $\approx76^\circ$ and a global M$_A$ of $\approx1.07$.