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Explore rapid simulation methods for large-scale structure formation in extended cosmologies through this 18-minute conference lecture from the Erwin Schrödinger International Institute workshop on cosmic large-scale structure theory and numerics. Learn how studying large-scale structure formation enables testing of fundamental cosmological concepts including dark energy nature, dark matter paradigms, and Modified Gravity theories with screening mechanisms that can circumvent classical General Relativity tests. Discover innovative approaches to accelerate the traditionally slow, non-linear numerical simulations required for theoretical predictions in extended cosmologies by combining analytical approximations with simulation methods. Examine the Hi-COLA code development for rapidly simulating structure formation in Horndeski gravity, and understand how informing numerical methods with analytical insights creates efficient "abbreviations" of the solution-finding process. Gain insights into advanced data extraction techniques from simulations and explore prospects for enhancing understanding through statistical methods that extend beyond traditional 2-point statistics approaches.
