  We use simulated strongly lensed gravitational wave events from the Einstein
Telescope to demonstrate how the luminosity and angular diameter distances,
$d_L(z)$ and $d_A(z)$ respectively, can be combined to test in a model
independent manner for deviations from the cosmic distance duality relation and
the standard cosmological model. In particular, we use two machine learning
approaches, the Genetic Algorithms and Gaussian Processes, to reconstruct the
mock data and we show that both approaches are capable of correctly recovering
the underlying fiducial model and can provide percent-level constraints at
intermediate redshifts when applied to future Einstein Telescope data.
