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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 constraints. 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. Recent advances in machine learning and differentiable modeling offer new approaches to improving these simulations and connecting them to observations, from GPU acceleration to field-level inference techniques that bypass traditional summary statistics. In this talk, I will explore how integrating ML and related optimization techniques with 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.