Increasing data volumes, pushing to non-linear scales, create opportunities for machine learning in cosmology. One primary challenges is the inverse problem implicitly defined through simulations. Neural simulation-based inference is increasingly being recognized as a tool.

I will review this technique and present some work both on observational data as well as on methodological development, specifically multi-fidelity inference. In the second part of the talk, I will present recent work on probabilistic identification of cosmic voids.