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

We use simulated data from strongly lensed gravitational wave events from the Einstein Telescope to forecast constraints on the cosmic distance duality relation, also known as the Etherington relation, which relates the luminosity and angular diameter distances $d_L(z)$ and $d_A(z)$ respectively. In particular, we present a methodology to make robust mocks for the duality parameter $\eta(z)\equiv \frac{d_L(z)}{(1+z)^2 d_A(z)}$ and then we use Genetic Algorithms and Gaussian Processes, two stochastic minimization and symbolic regression subclasses of machine learning methods, to perform model independent forecasts of $\eta(z)$. We find that both machine learning approaches are capable of correctly recovering the underlying fiducial model and provide percent-level constraints at intermediate redshifts when applied to future Einstein Telescope data.