Abstract
Numerical modeling of 3D non-local thermodynamic equilibrium (non-LTE) radiative transfer is a significant computational bottleneck in solar physics. We introduce a fast, accurate surrogate model using Graph Neural Networks (GNNs) to solve 3D atomic-level populations. The solar atmosphere is represented as a directed graph where nodes encode local physical properties (such as temperature, velocity, and magnetic field) and edges encode geometric distances. An Encode-Process-Decode GNN architecture propagates information across the 3D domain, accounting for both horizontal and vertical radiative coupling. The model achieves inference speeds approximately $10^6$ times faster than traditional iterative solvers while showing high accuracy (>0.99 correlation) with Multi3D in the photosphere and mid-chromosphere, facilitating efficient and routine 3D non-LTE inversions.
Figure 1: Schematic representation of the 3D graph topology and connectivity scheme. Red nodes indicate the central column where atomic populations are inferred, while blue nodes represent the surrounding physical context required to capture non-local 3D radiative transfer effects. This illustration corresponds to ±2\pm 2 neighbors, stride S=1S=1, and radii R=3R=3. (a) Isometric 3D view of a sample subvolume. (b) Top-down (XY) projection illustrating the “star-like” connectivity. (c) Side (XZ) projection showing the vertical stratification and how radii RR and distance to the center affects the connectivity.
