Machine learning forecasts of the cosmic distance duality relation with strongly lensed gravitational wave events

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.