Accelerating 3D Non-LTE Synthesis with Graph Neural Networks

Spectropolarimetric interpretation of chromospheric lines requires solving the radiative transfer problem under non-local thermodynamic equilibrium (non-LTE) conditions. This means computing atomic-level populations self-consistently with the radiation field. While traditional inversion codes employ 1.5D approximations, they neglect horizontal radiative transfer, which can be significant near magnetic structures and in the chromosphere. We present a method to solve 3D atomic-level populations using Graph Neural Networks (GNNs), extending prior 1.5D work to the full 3D domain. By discretizing the solar atmosphere as a directed graph, in which nodes encode physical properties and edges encode spatial distances, an Encode-Process-Decode GNN propagates information to efficiently capture radiative coupling. The network is trained on a Bifrost simulation using Ca II populations from Multi3D as ground truth. The trained GNN accurately predicts populations of the five-level Ca II atom plus continuum. Correlations exceed 0.99 in the photosphere and mid-chromosphere; errors in the upper chromosphere remain unbiased. Inference is $\sim 10^6$ times faster than traditional iterative solvers. Spectral synthesis of the Ca II 8542 \AA\ line yields intensity profiles with $< 2 \%$ mean residuals relative to the full 3D solution. This framework bypasses the computational bottleneck of iterative solvers while preserving essential non-LTE physics, including horizontal transfer, paving the way toward routine 3D non-LTE inversions.