  Supermassive black holes require a reservoir of cold gas at the centre of
their host galaxy in order to accrete and shine as active galactic nuclei
(AGN). Major mergers have the ability to drive gas rapidly inwards, but
observations trying to link mergers with AGN have found mixed results due to
the difficulty of consistently identifying galaxy mergers in surveys. This
study applies deep learning to this problem, using convolutional neural
networks trained to identify simulated post-merger galaxies from
survey-realistic imaging. This provides a fast and repeatable alternative to
human visual inspection. Using this tool, we examine a sample of ~8500 Seyfert
2 galaxies (L[OIII] ~ $10^{38.5 - 42}$ erg/s) at z < 0.3 in the Sloan Digital
Sky Survey and find a merger fraction of $2.19_{-0.17}^{+0.21}$% compared with
inactive control galaxies, in which we find a merger fraction of
$2.96_{-0.20}^{+0.26}$%, indicating an overall lack of mergers among AGN hosts
compared with controls. However, matching the controls to the AGN hosts in
stellar mass and star formation rate reveals that AGN hosts in the star-forming
blue cloud exhibit a ~$2\times$ merger enhancement over controls, while those
in the quiescent red sequence have significantly lower relative merger
fractions, leading to the observed overall deficit due to the differing
$M_{\ast} - $SFR distributions. We conclude that while mergers are not the
dominant trigger of all low-luminosity, obscured AGN activity in the nearby
Universe, they are more important to AGN fuelling in galaxies with higher cold
gas mass fractions as traced through star formation.
