Time evolution of the magnetic field in our fiducial CHEM_MHD simulation at R < 500 pc and |z| < 100 pc. Top: the full lines are the volume-weighted magnetic fields (Eq. (13)) averaged over the indicated density range. The black dashed line is the mass-weighted magnetic field averaged over all densities (Eq. (13)). The figure shows that the field grows in time starting from the initial seed as a result of dynamo action (Sect. 6). Bottom: integrated magnetic energy in the same density regimes. We note that while the denser part of the ISM has higher magnetic field values, most of the magnetic energy is actually in the low density regime.