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