  Currently available star cluster catalogues from HST imaging of nearby
galaxies heavily rely on visual inspection and classification of candidate
clusters. The time-consuming nature of this process has limited the production
of reliable catalogues and thus also post-observation analysis. To address this
problem, deep transfer learning has recently been used to create neural network
models which accurately classify star cluster morphologies at production scale
for nearby spiral galaxies (D < 20 Mpc). Here, we use HST UV-optical imaging of
over 20,000 sources in 23 galaxies from the Physics at High Angular Resolution
in Nearby GalaxieS (PHANGS) survey to train and evaluate two new sets of
models: i) distance-dependent models, based on cluster candidates binned by
galaxy distance (9-12 Mpc, 14-18 Mpc, 18-24 Mpc), and ii) distance-independent
models, based on the combined sample of candidates from all galaxies. We find
that the overall accuracy of both sets of models is comparable to previous
automated star cluster classification studies (~60-80 per cent) and show
improvement by a factor of two in classifying asymmetric and multi-peaked
clusters from PHANGS-HST. Somewhat surprisingly, while we observe a weak
negative correlation between model accuracy and galactic distance, we find that
training separate models for the three distance bins does not significantly
improve classification accuracy. We also evaluate model accuracy as a function
of cluster properties such as brightness, colour, and SED-fit age. Based on the
success of these experiments, our models will provide classifications for the
full set of PHANGS-HST candidate clusters (N ~ 200,000) for public release.
