  With the advent of next-generation surveys and the expectation of discovering
huge numbers of strong gravitational lens systems, much effort is being
invested into developing automated procedures for handling the data. The
several orders of magnitude increase in the number of strong galaxy-galaxy lens
systems is an insurmountable challenge for traditional modelling techniques.
Whilst machine learning techniques have dramatically improved the efficiency of
lens modelling, parametric modelling of the lens mass profile remains an
important tool for dealing with complex lensing systems. In particular, source
reconstruction methods are necessary to cope with the irregular structure of
high-redshift sources. In this paper, we consider a Convolutional Neural
Network (CNN) that analyses the outputs of semi-analytic methods which
parametrically model the lens mass and linearly reconstruct the source surface
brightness distribution. We show the unphysical source reconstructions that
arise as a result of incorrectly initialised lens models can be effectively
caught by our CNN. Furthermore, the CNN predictions can be used to
automatically re-initialise the parametric lens model, avoiding unphysical
source reconstructions. The CNN, trained on reconstructions of lensed S\'ersic
sources, accurately classifies source reconstructions of the same type with a
precision $P > 0.99$ and recall $R > 0.99$. The same CNN, without re-training,
achieves $P=0.89$ and $R=0.89$ when classifying source reconstructions of more
complex lensed HUDF sources. Using the CNN predictions to re-initialise the
lens modelling procedure, we achieve a 69 per cent decrease in the occurrence
of unphysical source reconstructions. This combined CNN and parametric
modelling approach can greatly improve the automation of lens modelling.
