Motivated by recent high resolution results on the inversion domain boundaries (IDB) in gallium nitride, we refine by ab initio DFT calculations the well established atomic model IDB * derived by Northrup et al. This allows us to recover these experimental results obtained by coherent x-ray diffraction and showing small additional shifts of the polarity domains, in particular 8 pm shift along the hexagonal direction. The influence of boundary conditions and electrostatic fields (IDB-IDB and IDB-surface interactions) on the results and the existence of metastable solutions is carefully discussed to stress the accuracy of the method. These results demonstrate a cross-talk between advanced characterization tools and state-of-the-art ab initio calculations that opens perspectives for the structural analysis of defects in the picometer range.