  Modelling the mass distributions of strong gravitational lenses is often
necessary to use them as astrophysical and cosmological probes. With the high
number of lens systems ($>10^5$) expected from upcoming surveys, it is timely
to explore efficient modeling approaches beyond traditional MCMC techniques
that are time consuming. We train a CNN on images of galaxy-scale lenses to
predict the parameters of the SIE mass model ($x,y,e_x,e_y$, and $\theta_E$).
To train the network, we simulate images based on real observations from the
HSC Survey for the lens galaxies and from the HUDF as lensed galaxies. We
tested different network architectures, the effect of different data sets, and
using different input distributions of $\theta_E$. We find that the CNN
performs well and obtain with the network trained with a uniform distribution
of $\theta_E$ $>0.5"$ the following median values with $1\sigma$ scatter:
$\Delta x=(0.00^{+0.30}_{-0.30})"$, $\Delta y=(0.00^{+0.30}_{-0.29})" $,
$\Delta \theta_E=(0.07^{+0.29}_{-0.12})"$, $\Delta e_x = -0.01^{+0.08}_{-0.09}$
and $\Delta e_y = 0.00^{+0.08}_{-0.09}$. The bias in $\theta_E$ is driven by
systems with small $\theta_E$. Therefore, when we further predict the multiple
lensed image positions and time delays based on the network output, we apply
the network to the sample limited to $\theta_E>0.8"$. In this case, the offset
between the predicted and input lensed image positions is
$(0.00_{-0.29}^{+0.29})"$ and $(0.00_{-0.31}^{+0.32})"$ for $x$ and $y$,
respectively. For the fractional difference between the predicted and true time
delay, we obtain $0.04_{-0.05}^{+0.27}$. Our CNN is able to predict the SIE
parameters in fractions of a second on a single CPU and with the output we can
predict the image positions and time delays in an automated way, such that we
are able to process efficiently the huge amount of expected lens detections in
the near future.
