Strongly lensed supernovae as a self-sufficient probe of the distance
  duality relation
  The observation of strongly lensed Type Ia supernovae enables both the
luminosity and angular diameter distance to a source to be measured
simultaneously using a single observation. This feature can be used to measure
the distance duality parameter $\eta(z)$ without relying on multiple datasets
and cosmological assumptions to reconstruct the relation between angular and
luminosity distances. In this paper, we show how this can be achieved by future
observations of strongly lensed Type Ia systems. Using simulated datasets, we
reconstruct the function $\eta(z)$ using both parametric and non-parametric
approaches, focusing on Genetic Algorithms and Gaussian processes for the
latter. In the parametric approach, we find that in the realistic scenario of
$N_{\rm lens}=20$ observed systems, the parameter $\epsilon_0$ used to describe
the trend of $\eta(z)$ can be constrained with the precision achieved by
current SNIa and BAO surveys, while in the futuristic case ($N_{\rm
lens}=1000$) these observations could be competitive with the forecast
precision of upcoming LSS and SN surveys. Using the machine learning approaches
of Genetic Algorithms and Gaussian processes, we find that both reconstruction
methods are generally well able to correctly recover the underlying fiducial
model in the mock data, even in the realistic case of $N_{\rm lens}=20$. Both
approaches learn effectively from the features of the mock data points,
yielding $1\sigma$ constraints that are in excellent agreement with the
parameterised results.
