Cosmological hydrodynamical simulations are essential for understanding the interplay between dark matter and baryons, yet they remain computationally expensive and struggle to fully reproduce observational data. At the same time, tensions in key cosmological parameters, such as σ₈, raise the question of whether new fundamental physics or baryonic feedback effects are responsible. In this talk, I will explore how integrating ML techniques into hydrodynamical simulations can enhance our ability to extract cosmological information, discuss the challenges and limitations of these methods, and outline the path toward a more efficient and robust framework for large-scale structure inference. In particular, I will highlight efforts towards "solver-in-loop" techniques enabled by end-to-end differentiable simulation pipelines could be used to either greatly accelerate simulations or discover previously unknown physics and/or survey systematics.