Modeling assembly bias with machine learning and symbolic regression

Upcoming 21cm surveys will map the spatial distribution of cosmic neutral hydrogen (HI) over unprecedented volumes. Mock catalogues are needed to fully exploit the potential of these surveys. Standard techniques employed to create these mock catalogs, like Halo Occupation Distribution (HOD), rely on assumptions such as the baryonic properties of dark matter halos only depend on their masses. In this work, we use the state-of-the-art magneto-hydrodynamic simulation IllustrisTNG to show that the HI content of halos exhibits a strong dependence on their local environment. We then use machine learning techniques to show that this effect can be 1) modeled by these algorithms and 2) parametrized in the form of novel analytic equations. We provide physical explanations for this environmental effect and show that ignoring it leads to underprediction of the real-space 21-cm power spectrum at $k\gtrsim 0.05$ h/Mpc by $\gtrsim$10\%, which is larger than the expected precision from upcoming surveys on such large scales. Our methodology of combining numerical simulations with machine learning techniques is general, and opens a new direction at modeling and parametrizing the complex physics of assembly bias needed to generate accurate mocks for galaxy and line intensity mapping surveys.