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

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