Many inverse problems are only defined implicitly through simulations. In such cases, one can use machine learning to perform parameter inference. After a quick introduction to this implicit-likelihood inference, I will concentrate on the application to the universe’s large-scale structure. The example I will present is a constraint on neutrino mass using the cosmic voids. In the final part, I will talk about the immense challenge that we face in cosmology: computational cost of accurate simulations. One approach to this problem is multi-fidelity learning, for which I will present one approach we have developed.