Reconstruction of a 3D magnetic field within a cube of side L = 3 = kpc. Top: the ground truth; a uniform field parallel to the x − y plane with magnitude 5 μG, plus a turbulent, random, field with an RMS magnitude of 1 μG, corresponding to λ = 0.2 in Eq. (10). Middle: local data sampled randomly, with a constant mean sampling rate (600 pc)⁻¹. The colormap is saturated at the maximum magnitude that appears in Fig. 1a. Bottom: the mean of the approximating posterior distribution attained via the geoVI algorithmn based on the data provided in Fig. 1b.