Machine learning algorithms are very good at approximating very general functions. Sometimes we want to constrain some parameters (e.g. cosmological parameters) given a set of observations. For standard observables (e.g. galaxy clustering) the likelihood function behind the data is known. By sampling it, constraints on the parameters can be placed.
It is also possible to use neural networks to approximate the function that relates an observable (with unknown likelihood) to the value of the cosmological parameters.
We have used this method to constrain the value of the cosmological and astrophysical parameters from measurements of the star-formation rate density (SFRD) of the SIMBA simulations from z=0 to z=7.